THERMO SAMPLE PROBLEMS

1. 40x
8.1
32x
x
FCx
32)C(8.1F
8.1
32F
C
Conversion







MECHANICAL ENGINEERING REVIEW
Problem Set no. 1
MULTIPLE CHOICE
1. A spherical tank is full of water that has a mass of 10 000 kg. If the outside diameter of the tank is 2722 mm,
how thick is the wall of the tank?
mm24
2
2674-2722
t
mm2674m2.6742(1.337)d
m337.1r
3
r4
V
m10
1000
000,10
V
V
m
3
3






π
ρ
2. A cylindrical tank is filled with water at the rate of 5000 Gal/min. The height of water in the tank after 15 minutes
is 20.42 ft. What is the diameter of the tank? (Note: 1 ft3 = 7.481 Gallons)
ft25D
ft20.42H;HD
4
V
ft10,025.4Gallons75000)15(5000V
2
3



π
3. At what temperature in which the reading in Fahrenheit scale is the same as the Centigrade scale.
4. A new temperature scale is desired with freezing point of water at 0X and boiling occurring at 1000X. Derive
the conversion between C and X and what is 0K in X.
2730X
0)273(10X
-273C
273CK0
273CK
bmxy
10m
10
0100
01000











2. Newton10x9.1
)10(29.5
)10)(11.9)(10)(66.1)(10(67.6
F
Newton
r
mGm
F
43
11
312711
g
2
21
g





5. A pressure gage at elevation 8 m on the side of a tank containing a liquid reads 57.4 KPa. Another gage at
elevation 5 m reads 80 KPa. Compute the specific weight and density of the liquid. (use g = 9.81 m/sec2)
3
3
m
kg
767.9
1000
g
m
KN
53.7
)58()804.57(
)h(P





ρ
ρ
γ
γ
γ
ΔγΔ
6. An open tank contains 5 m of water covered with 2 m of oil ( = 8 KN/m3). Find the absolute pressure at the at
the bottom of the tank. (Assume Patm = 101 KPa)
KPa166.05P
P)81.9(5)8)(2(101
Bottom
Bottom


7. A skin diver wants to determine the pressure exerted by the water on her body after a descent of 35 m to a
sunken ship. The specific gravity of seawater is 1.02 times that of pure water. Determine the pressure in KPa.
 )81.9)(02.1(350P
8. A water storage tank contains liquid and vapor in equilibrium at 250C,(l = 799.23 m3/kg; v = 19.95 m3/kg).The
distance from the bottom of the tank to the liquid level is 10 m. What is the difference in pressure reading
between the top of the tank and the bottom of the tank if the vapor pressure is 3,973 KPa. (Assume g = 9.81
m/sec2)
KPa4.784,051.4)-3,973(P
KPa4,051.4)10(
1000
)81.9(23.799
973,3PBottom


Δ
9. Compute the gravitational force between a proton ( m = 1.66 x 10 -27 kg) and an electron (m = 9.11 x 10-31 kg)in
an atom whose radius of electron orbit is 5.29 x 10-11 m.
10. A pressure in the cylinder in the figure varies in the following manner with volume, P = C/V2. If the initial pressure
is 500 KPa, initial volume is 0.05 m3 and the final pressure is 200 KPa, find the work done by the system.
KJ9W
m08.0V
V200)05.0(500
VPVP
2n;CPV
n1
VPVP
dVPW
systemNonFlowaFor
3
2
2
2
2
2
22
2
11
2
1122







 

3. 11. If the F scale is twice the C scale, what will be the corresponding reading in each scale?









320F
160
8.12
32
C
32C8.1C2
C2F
32C8.1F
8.1
32F
C
12. A cylindrical tank 2 m diameter, 3 m high is full of oil. If the specific gravity of oil is 0.9, what is the mass of oil in
the tank? (8482.3 kg)
kg3.8482)3(900m
V
m
m
kg
900
1000
9.0
S
m33)2(
4
HD
4
V
3
water
322
cylinder






π
ρ
ρ
ρ
ρ
ρ
π
ππ
13. 10 liters of an incompressible liquid exert a force of 20 N at the earth’s surface. What force would 2.3 Liters of
this liquid exert on the surface of the moon? The gravitational acceleration on the surface of the moon is 1.67
m/sec2.
 
N783.0)67.1(
1000
3.2
874.203F
moontheofsurfacetheOn
m
kg
874.203
N81.9
1000
)0.10(
20
kg
L1000
m1
)0.10(Vm
V
m
maF
3
3






















14. If the temperature inside a furnace is 700 K, what is the corresponding reading in F? (800.6)
Solution:
t = 700 – 273 = 427C
F = (427)(1.8) + 32
F = 800.6F
15. A storage tank contains oil with a specific gravity of 0.88 and depth of 20 m. What is the hydrostatic pressure at
the bottom of the tank in kg/cm2.(1.7)
Solution:
Using: g = 9.81 m/sec2
KPa656.172
1000
)20)(81.9)(1000(88.0
0P 
P = 1.7 kg/cm2

4. h
 
meters25.368h
1000
h0mg
)1000(2
085m
PEKE
2







 
 ΔΔ
16. A hiker carrying a barometer that measures 101.3 KPa at the base of the mountain. The barometer reads 85
KPa at the top of the mountain. The average air density is 1.21 kg/m3. Determine the height of the mountain.
m1373h
)81.9(21.1
1000)853.101(
h
g
1000)PP(
h
hhh
)hh(PP
dhdP
21
12
1212








ρ
γ
γ
17. Water runs through a water main of cross sectional area of 0.4 m2 with a velocity of 6 m/sec. Calculate the
velocity and mass flow rate of the water in the pipe when the pipe tapers down to a cross sectional area of 0.3
m2. ( = 1000 kg/m3)
sec
m
8
A
vA
v
vAvA
sec
kg
24006)4.0(1000m
mvA
mmm
2
11
2
2211
11
21





18. The 600 kg hammer of a pile driver is lifted 2 m above the piling head. What is the change in potential energy?
If the hammer is released, what will be its velocity at the instant it strikes the filing? Local g =9.65 mps2.(11.58
KJ; 6.21 mps)
m = 600 kg
Z = 2 m
g = 9.65 m/sec2
KJ58.11PE
KJ
1000
Zmg
PE



KE = PE
sec
m
21.6
600
)2000(58.11
v
0v
58.11
)1000(2
)vv(m
f
i
2
i
2
f




19. A lump of ice falls from an aero plane as it comes into land. If the ice hits the ground with a vertical speed of 85
m/sec, what was the height of the plane when the ice fell off? (use g = 9.81 m/sec2)

5. KW475.2880-0.275-290.752W
PE-KE-h-QW
KW2Q
0PE
KW275.0
)1000(2
)v-m(v
KE
KW75.290)hh(mh
WPEKEhQ
2
1
2
2
12







20. 5 kg of brass of specific heat 0.39 KJ/kg -C at a temperature of 176C is dropped into a 1.2 kg of water at 14C.
Find the resulting temperature of the mixture. (CPW = 4.187 KJ/kg -C)
C4.40t
)14t)(187.4(2.1)t176)(39.0(5
)tt(Cm)tt(Cm
QQ
by waterabsorbedHeatbrassbyrejectedHeat
C-kg
KJ
187.4C
C-kg
KJ
0.39C
kg5m
kg2.1m
1wPWw1BPBB
WB
PW
PB
B
w











21. How much heat is removed to make ice of mass m = 0.720 kg at -10C from a liquid at 15C.
Specific heat of ice = 2.22 KJ/kg-C
Specific heat of water = 4.19 KJ/kg-C
Freezing point temperature of water = 0C
hF of ice = 334.9 KJ/kg
Answer: 302 KJ
 
KJ302Q
10)2.22(0(334.9)0)-4.19(150.720Q
heatsensible)100(mCQ
heatlatent)h(mQ
heatsensible)015(mCQ
QQQQ
pi3
F2
pw1
321






22. A steam turbine receives superheated steam at 1.4 MPa and 400C (h1 = 3257.5 KJ/kg). The steam leaves the
turbine at 0.101 MPa and 100C (h2 = 2676 KJ/kg).The steam enters the turbine at v1 = 15 m/sec and exits at
v2 = 60 m/sec. The elevation difference between entry and exit ports is negligible. The heat loss through the
turbine walls is 2 KW. Calculate the power output if the mass flow through the turbine is 0.5 kg/sec.
23. Steam with a flow rate of 1360 kg/hr enters an adiabatic nozzle at 1378 KPa, 3.05 m/sec with a specific volume
of 0.147 m3/kg and with a specific internal energy of 2510 KJ/kg. The exit conditions are, P = 137.8 KPa, specific
volume = 1.099 m3/kg, and internal energy = 2263 KJ/kg. Determine the exit velocity in m/sec.
Given:
m = 1360 kg/hr = 0.377 kg/sec P2 = 137.8 KPa
P1 = 1378 KPa 2 = 1.099 m3/kg
v1 = 3.05 m/sec U2 = 2263 KJ/kg
1 = 0.147 m3/kg
U1 = 2510 KJ/kg
1 2
For Adiabatic Q = 0 andfor
a Nozzle W = 0

6. m/sec3.788v
KJ/kg9.2401)099.1)(8.137(2263h
KJ/kg6.2712)147.0)(1378(2510h
PUh
v)hh)(1000(2v
)hh(
)1000(2
vv
hKE
00KEh0
WPEKEhQ
2
2
1
2
1212
12
2
1
2
2











24. A small steam turbine operating at part load produces 110 KW output with a steam flow rate of 0.25 kg/sec.
Steam at 1.4 MPa, 250C is throttled to 1.1 MPa before entering the turbine, and the turbine exhaust pressure
is 10 KPa. Find the steam quality (or temperature, if superheated) at the turbine outlet. (x2 = 96%)
From table 3 at 1.4 MPa and 250C: h = 2927.2 KJ/kg
From table 2 at 10 KPa (0.010 MPa): hf = 191.83 KJ/kg; hfg = 2392.8 KJ/kg
%96x
96.0
8.2392
191.83-2487.2
x
)h(xhh
kg
KJ
2487.2h
m
110
-hh
)h-m(h110
h-W
0PEand0KE;0Q
WPEKEhQ
kg
KJ
2.2927hh
sec
kg
25.0m
3
3
fgf
3
23
32
21











25. A throttling calorimeter is connected to the de-superheated steam line supplying steam to the auxiliary feed
pump of a ship. The line pressure measures 2.5 MPa. The calorimeter pressure is 110 KPa and the temperature
is 150C. Determine the line steam quality.
From Superheated table, at 110 KPa and 150C, h2 = 2775.6 KJ/kg
From Saturated liquid and saturated vapor table
hf 1 = 962.11 KJ/kg; hf g = 1841.0 KJ/kg
h1 = hf 1 + x1(hf g1)
h1 = h2
%98.5x
985.0
0.1841
11.9626.2775
h
hh
x
1
1fg
1f1
1






1 2
3
Wt

7. 3
L
3
V
V
VV
VL
V
V
V
V
g
V
L
L
L
f
VL
VL
m029.0V
m056.0V
004193.0002222.0
)004193.0(085.0
V
004193.0
V
00222.0
V085.0
mm
3eq.
004193.0
V
m
m
V
v
2eq.
00222.0
V085.0
m
m
V
v
1eq.V085.0V
085.0VV















26. An engineering student wants to cool 0.25 kg of Omni Cola (mostly water) initially at 20C by adding ice that is
initially at -20C. How much ice should be added so that the final temperature will be 0C with all the ice melted,
if the heat capacity of the container neglected.
Cwater = 4.19 KJ/kg-C
Cice = 2.010 KJ/kg-C
hf of ice = 334.9 KJ/kg
Qcola = Qice
0.25(4.19)(20 – 0) = mice[(2.010)(0 + 20) + 334.9]
mice = 0.056 kg = 56 gram
27. 2.5 kg of brass of specific heat 0.39 KJ/kg-K at a temperature of 176C is dropped into a 1.2 liters of water at
14C. Find the resulting temperature of the mixture. (At 14C density of water is 999 kg/m3)
kg1988.1)999(
1000
2.1
mw 
Heat rejected by brass = Heat absorbed by water
2.5(0.39)(176 – t) = 1.1988(4.187)(t – 14)
171.6 – 0.975t = 5.02t – 70.3
t = 40.4C
28. An 85 Liters drum contains saturated water and water vapor at 370C.
a. Find the masses of each if their volumes are equal
b. Find the volume occupied by each if their masses are equal
From steam table at 370C
vf = 0.002222 m3/kg
vg = 0.004193 m3/kg
a.
VL = 0.0425 m3 ; VV = 0.0425 m3
kg14.10
004193.0
0425.0
m
004193.0
m
V
v
kg13.19
002222.0
0425.0
m
002222.0
m
V
v
V
V
V
g
L
L
L
f




b.

8. 29. An industrial power plant requires 1.5 kg of dry saturated steam per second at 165C for heating purposes. This
steam may be supplied from an extraction turbine which receives steam at 4 MPa and 380C and is exhausted
to a condenser at the rate of 0.8 kg/sec at 0.0034 MPa while rejecting 1400 KW to the cooling water. If the
mechanical efficiency of the turbine generator unit is 95% and the heat loss in the turbine casing is 10 KW,
calculate the power generated by the plant.
(Wo = 1540 KW)
h at 4 MPa and 380C = 3165.9 KJ/kg
hg at 165C = 2763.5 KJ/kg
hf at 0.0034 MPa = 109.84 KJ/kg
10 KW
1.5 kg/sec
165 C
0.8 kg/sec
1
2
3
4
Wt’
P1 = 4 Mpa
t1 = 380C
m = ______
QR = 1400 KW
h1
h2
h4
GP = Generator
Power
Generator Efficiency = 94%
KW14.1540W
KW1638.45W
Wt4)0.8(1859.8-)1.5(2763.5-10-)2.3(3165.9
turbinetheinbalanceenergyBy
kg
KJ
84.1859h
)84.1093h(8.01400
)hh(8.0Q
condenserbalanceenergyBy
sec
kg
3.20.81.5m
balancemassBy
OUTPUT
t
3
43R







30. Steam enters a turbine with a velocity of 1.5 m/sec and an enthalpy of 2093 KJ/kg and leaves with an enthalpy
of 1977 KJ/kg and a velocity of 91.5 m/sec. Heat losses are 8 KCal/min and the steam flow rate is 27 kg/min.
The inlet of the turbine is 3.5 m higher than its outlet. What is the work output of the turbine if the mechanical
losses is 15%
a) 32.4 KW b) 24.3 KW c) 34.2 K d) 48 KW

9. KW3.42.15)-49.77(1OutputPower
KW77.49)PEKEh(QW
WPEKEhQ
KW015.0
1000
)zz(mg
PE
KWKW2.52)hh(mh
KW883.1
)1000(2
)vv(m
KE
kg
KJ
1977h
kg
KJ
2093h
m-3.5z
0z
(rejected)KW56.0
sec60
min1
x
KCal
KJ
187.4x
min
KCal
8Q
sec
kg
45.0
min
kg
27m
sec
m
5.91v
sec
m
5.1v
12
12
2
1
2
2
2
1
2
1
2
1


















system)theondoneis(WorkKW24.67W
KW67.248.2)0.1785(-13W
KWIn
kg
KJ
2.138
26.1
101
86.4
546
)82()24(W
PP
-)U-(U-QW
0-0-)P-(P-)U-(U-QW
PE-KE-)(P-U-QW
WPEKE)(PUQ
kg/sec0.1785kg/min71.10)5.8(26.1Vm
V
m
1
1
2
2
12
112212



























31. An air compressor handles 8.5 m3/min of air with a density of 1.26 kg/m3 and a pressure of 101 KPaa and
discharges at 546 KPaa with a density of 4.86 kg/m3. The changes in specific internal energy across the
compressor is 82 KJ/kg and the heat loss by cooling is 24 KJ/kg. Neglecting changes in kinetic and potential
energies, find the work in KW.
32. Calculate the change of entropy per kg of air when heated from 300K to 600K while the pressure drops from
400 Kpa to 300 KPa. (S = 0.78 KJ/kg-K)
Given;
R = 0.287 KJ/kg-K
k = 1.4
T1 = 300K ; T2 = 600K
P1 = 400 KPa ; P2 = 300 KPal
1
2
1
2
p
P
P
lnR
T
T
lnCS Δ

10. 33. A certain mass of sulfur dioxide (SO2) is contained in a vessel of 0.142 m3 capacity, at a pressure and
temperature of 2310 KPa and 18C, respectively. A valve is open momentarily and the pressure falls
immediately to 690 KPa. Sometime later the temperature is again 18C and the pressure is observed to be 910
KPa. Estimate the value of specific heat ratio. (k = 1.29)
K92.86
T
P
P
T
T
P
T
P
CVAt
kg67.8
)291(13.0
)142.0(2310
m
RTmVP
13.0
64
3143.8
R
1
1
2
2
2
2
1
1
1
1111



















34. Two unequal vessel A and B are connected by a pipe with a valve. Vessel A contains 150 L of air at 2760 KPa
and 95C. Vessel B contains an unknown volume of air at 70 KPa and 5C. The valve is opened and when the
properties have been determined, it was found out that the pressure of the mixture is 1380 KPa and the
temperature is 45C. What is the volume of vessel B.(0.166 m3)
Given:
VA = 0.150 m3 ; PA = 2760 KPa ; TA = 95 + 273 = 368 K
PB = 70 KPa ; TB = 5 + 273 = 278 K
P = 1380 KPa ; T = 45 + 273 = 318 K
3
B
BB
BB
B
BB
B
A
AA
A
BA
BA
m116.0
)252.034.4(
)65.0125.1(
V
V252.0125.1V34.465.0
)278(R
)V(70
)368(R
)150.0(2760
)318(R
)V150.0(1380
RT
VP
m;
RT
VP
m;
RT
PV
m
mmm
VVV










35. A vessel of volume 0.2 m3 contains nitrogen at 101.3 KPa and 15C. If 0.2 kg of nitrogen is now pumped into
the vessel, calculate the new pressure when the vessel has returned to its initial temperature. For nitrogen: M
= 28; k = 1.399. (187 KPa) (Sample Prob. June 18, 2014)

11. C8.111t
K8.384
VP
VPT
T
T
VP
T
VP
C
T
PV
kg
kg
16
R
3143.8
M
M
3143.8
R
K-kg
KJ
52.0R
mT
VP
R
mRTPV
2
11
221
2
2
22
1
11
mol
1
11









KPa82.186
)2.0(28
273)43)(150.437(8.31
P
VV
V
mRT
P
K28827315T
massfinalkg437.00.20.237m
kg237.0
)27315(3143.8
28)2.0(3.101
m
K-kg
KJ
28
3143.8
R
RT
PV
m
mRTPV
addedNof(masskg0.2-m
K28827315TKPa;101.3P;m2.0V
:Given
2
12
2
2
1
2a
11
3
1














36. A certain perfect gas of mass 0.1 kg occupies a volume of 0.03 m3 at a pressure of 700 KPa and a temperature
of 131C. The gas is allowed to expand until the pressure is 100 KPa and the final volume is 0.2 m3. Calculate;
a) the molecular weight of the gas (16)
b) the final temperature
Given;
m = 0.1 kg ; V1 = 0.03 m3 ; P1 = 700 KPa ; T1 = 131 +273 = 404 K
P2 = 100 KPa ; V2 = 0.2 m3
37. An ideal gas with R = 2.077 KJ/kg-K and a constant k= 1.659 undergoes a constant pressure process during
which 527.5 KJ are added to 2.27 kg of the gas. The initial temperature is 38C. Find the S in KJ/K.
Given:
R = 2.077 KJ/kg-K; k = 1.659
Q = 527.5 KJ; m = 2.27 kg
T1 = 38 + 273 = 311 K
Process: P = C
Q = mCp(T2 – T1) ;
Kkg/KJ72.5
1k
RK
Cp 


K352T
mCp
Q
T 12 
K/KJ6.1
T
T
lnmCpS
1
2


12. 38. A certain perfect gas of mass 0.1 kg occupies a volume of 0.03 m3 at a pressure of 700 KPa and a temperature
of 131C. The gas is allowed to expand until the pressure is 100 KPa and the final volume is 0.02 m3. Calculate;
a) the molecular weight of the gas (16)
b) the final temperature (11.5C)
C7.15t
16
)2732t)(3143.8(1.0
)15.0(100
mRTVP
16M
M
)273131)(3143.8(1.0
)03.0(700
2
222







39. What is the weight of a 114 L tank of oxygen (O2) if the oxygen is pressurized to 1.4 MPa, and the tank itself
weighs 445N, and the temperature is 10C.
N29.44621.29445Wt
N29.212.17(9.81)W
kg17.2
)27310(26.0
)114.0(1400
m
mRTPV
K-kg
KJ
26.0
32
3143.8
R
2O







40. Assume 2 kg of O2 are mixed with 3 kg of an unknown gas. The resulting mixture occupies a volume of 1.2 m3
a) R and M of the unknown gas constituent
b) the volumetric analysis
c) the partial pressures
For O2: M = 32 ;k = 1.395
Given; mO2 = 2 kg; mx = 3 kg
V = 1.2 m3 ; P = 276 KPa; T = 338 K
a)
m = 5 kg
xO2 = 0.40 ; xx = 0.60
R = 0.1361 KJ/kg-K
R = .40(0.26) + 0.60(Rx)
Rx = 0.535 KJ/kg-K
Mx = 15.54 kg/kgm
b)
yO2 = 0.245 ; yx = 0.755
c) PO2 = .245(276) = 67.62 KPa ; Px = 0.755(276) = 208.38 KPa

13. kg91.1
)389.01(
)3(389.0
m
m)3(389.0m)389.0(
3m
m
389.0
mm
m
m
m
x
611.0389.1x
389.0
36
)28(50.0
x
231.0R
36)44(50.0)28(50.0M
M
My
x
50.0y
50.0y
2
22
2
2
22
22
2
2
2
2
2
N
NN
N
N
CON
NN
N
CO
N
ii
i
CO
N















41. How many kilograms of N2 must be mixed with 3.6 kg of CO2 in order to produce a gaseous mixture that is 50%
by volume of each constituents.
Gas M k
CO2 44 1.288
N2 28 1.399
42. Three moles of oxygen is compressed in a piston cylinder assembly in a reversible adiabatic process from a
temperature of 300 K and a pressure of 102 KPa until the final volume is one tenth the initial volume. Determine
the final temperature and the final pressure.
Given; T1 = 300 K ; P1 = 102 KPa ;
12 V
10
1
V  ; 10
V
V
2
1

1k
2
1
1k
2
1
1
2
V
V
V
V
T
T













 12 TT; ; k
2
k
1
12
k
22
k
11
V
V
PP;VPVP 
For Oxygen; R = 0.2598 KJ/kg-K; k = 1.395
T2 = 745K ; P2 = 2532.8 KPa
43. Two kilograms of helium operates on a three process cycle where the processes are constant volume (1 to 2);
constant pressure (2 to 3); and constant temperature (3 to 1). Given that P1 = 100 KPa, T1 = 300 K, and 1/3
= 5. Determine the pressure, specific volume and temperature around the cycle.
For Helium: R = 2.077 KJ/kg-K ; k = 1.666

14. Given:
P1 = 100 KPa ; T1 = 300 K ; 1/3 = 5
Processes:
1 to 2 (Isometric: V = C)
2 to 3 (Isobaric: P = C)
3 to 1 (Isothermal: T = C or PV = C)
44. Oxygen expands in a reversible adiabatic manner through a nozzle from an initial pressure and initial
temperature and with an initial velocity of 50 m/sec. there is a decrease of 38K in temperature across the
nozzle. Determine
a. the exit velocity
b. for inlet conditions of 410 KPa and 320 K, find the exit pressure.
Given:
v1 = 50 m/sec
T = 38 K
P1 = 410 KPa ; T1 = 320 K
Fpr O2: Cp = 0.918 KJ/kg-K ; k = 1.395
1 2
3311
3
1
3
3
1
3
2
3
1
1
1
PP
kg
m
245.1
5
231.6
5
5
kg
m
231.6
kg
m
231.6
100
)300(077.2
P
RT
υυ
υ
υ
υ
υ
υ
υ
υυ
P
P
T
T
1
2
1
2







21
K300TT
KPa5.500PP
KPa5.500
245.1
)231.6(100P
P
13
23
3
11
3



υ
υ
K5.1501T
100
5.500
300
P
P
TT
2
1
2
12


KPa4.262P
T
T
P
P
K28238-320T
K38TT
sec
m
259.4v
velocityexit)T-(T2000C-vv
)T-(T-C
2000
v-v
)T-(T-ChKE
0PEand;0W;0Q
WPEKEhQ
2
1k
k
1
2
1
2
2
12
2
12p
2
12
12p
2
1
2
2
12p


















15. 45. A throttling calorimeter is connected to the main steam line where the pressure is 1.75 MPa. The calorimeter
pressure is 90 KPa and 105C. Determine the main steam quality.
From steam table
Aat 1.75 MPa; hf = 878.50 KJ/kg ; hg = 2796.4 KJ/kg
At 90 KPa and 105C; h = 2687.55 KJ/kg
h1 = h at 1.75 MPa and unknown quality
h2 = h at 90 KPa and 105C
h1 = h2
h1 = hf1 + x1(hfg1) = h2
2687.55 = 878.5 + x1(2796.4 – 878.5)
x1 = 0.9432 = 94.32%
46. A cylinder fitted with a frictionless piston contains 5 kg of superheated water vapor at 1000 KPa and 250C.
The system is now cooled at constant pressure until the water reaches a quality of 50%. Calculate the work
done and the heat transferred.
47. A 0.5 m3 tank contains saturated steam at 300 KPa. Heat is transferred until the pressure reaches 100 KPa.
Determine the heat transferred and the final temperature.
T
105C

P1 = 1.75KPa
x1 = 94.32%
P2 = 90 KPa
1
2
W
Q
U
T
S
1
2
From SteamTable:
At 1000 KPa and 250C
(superheated)
h = 2942.6 KJ/kg
U = 2709.90 KJ/kg
S = 6.9247 KJ/kg-C
 = 0.2327 m3/kg
At 1000 KPa and x = 50%
h = 1770.46 KJ/kg
U = 1672.64 KJ/kg
S = 4.3626 KJ/kg-C
 = 0.097784 m3/kg
tsat = 179.91C
Q
U
T

1
2
300 KPa
100 KPa
rejected)is(heatKJ88.5860Q
system)theondoneis(workKJ58.674)2327.097784.0)(1000(5)(mPPdmW
KJ3.51862709.9)-5(1672.64)U-m(UU
WUQ
KJ/kg1770.46h;KJ/kg1672.64U
KJ/kg2942.6h;KJ/kg9.2709U
2
1
12
12
22
11








16. Process: Constant Volume
W = 0
Q = U
Q = m(U2 – U1)
From Steam Table at P = 300 KPa (saturated vapor)
U1 = 2543.6 KJ/kg
1 = 0.6058 m3/kg
From steam Table at 100 KPa
g = 1.694 m3/kg ; f = 0.0010432 m3/kg
f g = g - f = 1.693 m3/kg
Ug = 2506.1 KJ/kg ; Uf = 417.36 KJ/kg ; Uf g = 2088.7 KJ/kg
2 = 1
2 = 0.0010432 + x2(1.693) = 0.6058
x2 = 0.357 = 35.7%
U2 = 417.36 + (0.357)(2088.7) = 1163.465 KJ/kg
Q = 0.825(1163.465 – 2543.6) = -1138.6 KJ
Q = 1138.6 KJ (Heat is rejected from the system)
48. A reversible nonflow constant volume process decreases the internal energy by 316.5 KJ for 2.3 kg of a gas for
which R = 0.47 KJ/kg-K and k = 1.35. For the process, determine
a. the work
b. the heat
c. the entropy change if the initial temperature is 478K
Given:
U = -316.5 KJ
m = 2.3 kg
R = 0.47 KJ/kg-K
k = 1.3
T1 = 478K
Solution
At V = C ; Q = U = mCv (T)
K390T
478)-(T2.3(1.567)316.5-Q
K-KJ/kg567.1
13.1
47.0
1k
R
Cv
2
2







a. W = PdV = 0
b. Q = -316.5 KJ
Q = 316.5 KJ (heat is rejected)
c.
kg825.0
6058.0
5.0
m
m
V

υ
K
KJ
733.0
478
390
ln)567.1(3.2
T
T
lnmCvS
1
2



17. n
1n
1
2
12n12n
n
1n
1
21
P
P
TT;
n1
nk
CvC);TT(mCQ
1
P
P
n1
nmRT
hQW


































 Δ
49. In a turbine 4500 kg/min of air expands polytropically from 425 KPa and 1360K to 101 KPa. The exponent n
= 1.45 for the process. Find the work done and the heat transfer.
Given:
m = 4500 kg/min ; P1 = 425 KPa; T1 = 1360K ; P2 = 101 KPa; PVn = C
n = 1.45 ; KE and PE are negligible
For Air: R = 0.287 KJ/kg-K; k = 1.4; Cp = 1.0045 KJ/kg-K; Cv = 0.7175 KJ/kg-K
rejected)is(heatKW2926Q
KW29261
425
101
)45.11(60
)1.45)(1360-5)(1.44500(0.717
Q
KW938.331
425
101
)45.11(60
)1360)(287.0)(4500(45.1
W
45.1
145.1
45.1
145.1





































50. Steam flows steadily through a turbine with a mass flow rate of 2.52 kg/sec. The inlet steam conditions are
7000 KPa and 500C. The exit steam pressure is 20 KPa and the expansion is isentropic. Determine the turbine
work in KW.
From Steam Table (superheated state)
At 7000 KPa and 500C
h1 = 3410.3
U1 = 3073.4
S1 = 6.7975
At S1 = S2 to 20 KPa (saturated mixture region)
h2 = 2239.45
U2 = 2110.47
x2 = 84.3%
51. In thermodynamics, a fixed quantity of mass selected for the purpose of study is called a:
a. system
b. closed system
c. open system
d. control volume
52. In order for a system to be in thermal equilibrium, which of the following properties must be the same throughout
the system?
a. mass
b. pressure
c. temperature
d. volume
m 1
Q = 0 m
2
W
KW54.2959)45.22393.3410(52.2W
kg/secinrateflowmasstheismwhere
KW)h-m(hW
KJ/kg)h--(hh-W
negligiblearePEandKE
adiabatic)(for0Q
WPEKEhQ
21
12







18. 53. A cycle consists of a series of processes that:
a. eventually return to the first state of the first process
b. are continually repeated
c. are always in equilibrium or quasi-equilibrium
d. none of these
54. A 0.5 m3 container is filled with a fluid whose specific volume is 0.001 m3/kg. At standard gravitational
acceleration, the contents of this container weigh:
a. 2010 N
b. 3220 N
c. 4905 N
d. 7830 N
N4905500(9.81)W
kg500
001.0
5.0
m
m
V
m5.0V 3




υ
55. Which temperature below is equivalent to 125 °F?
a. 52 °C
b. 125 °C
c. 602 °R
d. 315 K
C51.7
8.1
32125
8.1
32F
C 




56. On a day when the barometer reads 755 mm Hg, a tire pressure gage reads 204 KPa. The absolute pressure
in the tire is:
a. 100 KPa
b. 204 KPa
c. 1.54 m Hg
d. 2.29 m Hg
Hgm29.2KPa305
760
)325.101(755
204Pabs 






57. The fan pressure differential gage on an air handler reads 12 cm H2O. What is this pressure differential in Kilo
Pascals?
a. 0 kPa
b. 0.93 kPa
c. 1.18 kPa
d. 1.37 kPa
KPa18.1
OHcm33.10
KPa101.325
xOHm12.0
2
2 
58. At a pressure of 4 Mpa, the temperature at which liquid water boils is:
a. 29.0°C
b. 100.0°C
c. 143.6°C
d. 250.4°C
59. The specific volume of a system consisting of refrigerant 134a at 1,000 KPa is 0.01 m3/kg. The quality of the R-
134a is:
a. 12.62 %
b. 46.92 %
c. 68.32 %
d. Not applicable

19. %47x
)870.033.20(x870.010
kg
L
33.20g
kg
L
870.0f
Bar)(10KPa1000At




υ
υ
60. A system contains water at 2,000 KPa, 220°C. The phase of this water is:
a. Liquid
b. Liquid-vapor mixture
c. Vapor
d. Solid
61. KNA thermodynamic system contains water at 10 m3 of air whose pressure and temperature are 300 KPa,
127°C respectively. The weight for this system is:
a. 92 KN
b. 127 KN
c. 192 KN
d. 256 KN
KN92
1000
1)9367.5(9.8
1)9367.5(9.81)9367.5(9.8mgW
kg9367.5)10(75.936m
V
m
m
kg
75.936
C127andKPa300atTableSteamFrom
3




ρ
62. Air in a closed piston-cylinder device arranged to maintain a pressure of 400 KPa is heated from 27°C to 227°C.
Initially the volume of the air is 1 liter. What is the final air volume?
a. 0.5 liters
b. 0.00167 m3
c. 2.4 liters
d. 0.036 m3
3
2
2
2
2
1
1
m00167.0V
)273227(
V
)27327(
001.0
T
V
T
V





63. Propane gas (Pc = 4.26 MPa, Tc = 370 K) is maintained at 6.39 MPa and 444 K. How much volume does 1 kg
of this gas fill?
a. 8.78 liters
b. 12.3 liters
c. 13.1 liters
d. 15.7 liters
Liters1.13m131.0
6390
)444)(189.0(1
V
mRTPV
K-kg
KJ
189.0R
44M
Propane:8H3C
3




64. Air (Cp = 1.005 kJ/kg-k) is heated from 27°C to 327°C. How much does the specific internal energy of the air
change as a result of this heating?
a. 301.5 kJ/kg decrease
b. 301.5 kJ/kg increase
c. 215.4 kJ/kg decrease
d. 215.4 kJ/kg increase

20. kg
KJ
4.215)tt(CUΔ
K-kg
KJ
718.0287.0005.1C
RCC
12v
v
Vp



65. Steam at 1 MPa, 250°C is contained in a rigid vessel. It is now cooled to 25°C. The final quality (if applicable)
of the vessel contents is:
a. 0.54 %
b. 2.63 %
c. 27.8 %
d. Not applicable
%54.0x
0.001)-x(43.420.0010.233
43.42v
0.001L
)(SaturatedC25
5.2709U
kg
m
233.0
m
kg
4.2926
ed0(SuperheatC250t;KPa1000
tableSteamFrom
3
3









υ
υ
υ
ρ
66. The interaction that occurs between a system and its surroundings as the system executes a process, which is
the result of the system being at a temperature different from the surroundings, is:
a. Mass transfer
b. Heat transfer
c. Work transfer
d. None of these
67. Air is expanded from 1 MPa, 327°C to 200 kPa in a closed piston-cylinder device executing a PV1.2 = constant
process. The work produced during this process is:
a. 202.6 kJ/kg
b. 263.4 kJ/kg
c. 361.7 kJ/kg
d. 422.8 kJ/kg
kg
KJ
201.57W
K-kg
KJ
0.287R;kg1m
1
P
P
n1
nmRT
W
n
1n
1
21





















68. Oxygen (M = 32 kg/kg-mol) at 200 kPa, 27°C is contained in a piston-cylinder device arranged to maintain a
constant pressure. How much work is produced by this system when it is heated to 227°C?
a. 0 kJ/kg
b. 11.2 kJ/kg
c. 37.1 kJ/kg
d. 52.0 kJ/kg

21. kg
KJ
182)273127(445.0U
445.0228.0683.0C
RCC
683.0C
)273127(C2.273
tCh
Kkg
KJ
228.0
4.36
3143.8
R
v
vp
p
p
p








kg
KJ
52)TT(mRW
(Nonflow )Isobaric)VV(PW
K-kg
KJ
26.0
32
3143.8
R
12
12



69. A 1000 kg automobile accelerates from 10 km/hr to 120 km/hr. How much work does this require?
a. 0 kJ
b. 501 kJ
c. 552 kJ
d. 80 kJ
sec
m
33.33v
sec
m
78.2v
KJ
)1000(2
)vv(m
W
2
1
2
1
2
2




70. Steam at 1 MPa, 300°C flows through a 30 cm diameter pipe with an average velocity of 10 m/s. The mass flow
rate of this steam is:
a. 0.731 kg/s
b. 2.74 kg/s
c. 3.18 kg/s
d. 3.78 kg/s
sec
kg
739.2Avm
m30.0d
d
4
A
m
kg
3.8750
C300tKPa;1000P
TableSteamromF
2
3





ρ
π
ρ
71. Refrigerant-134a flows through a pipe at 800 KPa, 50°C. The specific flow work required to move this fluid
through a cross-section of the pipe is:
a. 22.84 kJ/kg
b. 31.60 kJ/kg
c. 37.21 kJ/kg
d. 40.70 kJ/kg









kg
KJ
84.22
1000
547.28
800PVE
kg
L
28.547
ed)(SuperheatC50t;KPa800P
TableR134aFrom
f
υ
72. A mixture of ideal gases has an apparent molecular weight of 36.4 kg/kg-mole and a specific enthalpy of 273.2
kJ/kg when the temperature is 127 °C. The specific internal energy of this gas mixture is:
a. 98.72 kJ/kg
b. 153.1 kJ/kg
c. 181.8 kJ/kg
d. 273.2 kJ/kg

22. kg
KJ
71.298W
NonFlow
n1
)TT(mR
W
65.1n
P
P
T
T
K979273206T;KPa2000P
K30027327T;KPa100P
12
n
1n
1
2
1
2
22
11
















72. A 12 V DC electrical motor draws a current of 18 amps. How much work does this motor produce over a 10-
minute period of operation?
a. 97.42 kJ
b. 129.6 kJ
c. 216.0 kJ
d. 318.2 kJ
73. Air at 1 MPa, 27°C is contained in a piston-cylinder device that is arranged to maintain a constant pressure.
How much heat is required to raise the temperature of this air to 527°C?
a. 180 KJ/kg
b. 370 KJ/kg
c. 502 KJ/kg
d. 1040 KJ/kg
kg
KJ
25.502WUΔQ
5.143)27527(287.0W
358.75)27527(7175.0UΔ
kg
KJ
25.502)27527(0045.1)TT(CQ 12p




74. Two kilograms of steam at 2 MPa, 250° C are contained in a rigid vessel. How much heat must be removed from
this vessel to cool it to 25°C?
a. 5030 kJ
b. 2512 kJ
c. -2512 kJ
d. -5030 kJ
KJ-5137.7Q
75.110U
0025.0x
8.2409U
36.43
88.104U
001003.0
11144.01;C25At
11144.0
kg
KJ
6.2679U
C250t;KPa2000At
2
2
g
g
f
f
1
1











υ
υ
υ
υ
75. Air is compressed in a piston-cylinder device. Using constant specific heats and treating the process as internally
reversible, the amount of work required to compress this air from 100 KPa, 27°C to 2000 KPa, 706°C is:
a. -298.7 kJ/kg
b. -512.2 kJ/kg
c. 721 kJ/kg
d. 103 kJ/kg
76. Air enters an adiabatic, steady-flow turbine at 1 MPa, 527° C through a 1m2 duct with a velocity of 100 m/s. The air

23. leaves the turbine at 100 kPa, 157C. The mass flow rate of the air is:
a. 87.4 kg/s
b. 137.3 kg/s
c. 327.2 kg/s
d. 435.34 kg/s
kg/sec34.435100)1(36.4m
36.4
)273527(287.0
1000
Avm
RT
P
1






ρ
ρ
ρ
77. Air enters a steady state, steady-flow turbine at 1,000 KPa, 550°C through a 1m2 duct with a velocity of 100 m/s.
The air leaves this turbine at 100 KPa, 200°C through a duct of the same size. Determine the work produced by this
Turbine for an internally reversible process.
a. 107.62 MW
b. 102.67 MW
c. 106.27 MW
d. 201.71 MW
KW107,618.2W
1000
zz
mgPEΔ
2(1000)
vv
mKEΔ
)TT(mChΔ
n1
nk
CC
)TT(mCQ
WPEΔKEΔhΔQ
32.1n
P
P
T
T
sec
m
8.574v
m
kg
74.0
RT
P
Avm
sec
kg
4.423m
m
kg
23.4
RT
P
sec
m
100v1;m1A;Avm
K473273200TKPa;100P
K823273550TKPa;1000P
12
2
1
2
2
12p
vn
12n
n
1n
1
2
1
2
2
3
2
2
2
22
3
1
1
1
2
22
11






 
































ρ
ρ
ρ
ρ
78. Steam at 4 MPa, 400° C enters a steady-flow, adiabatic turbine through a 20 cm-diameter-pipe with a velocity of 20
m/s. It leaves this turbine at 50 kPa with a quality of 80% through a 1 m-diameter pipe. What is the velocity of the
steam as it leaves the turbine?
a. 10.3 m/s
b. 28.2 m/s
c. 32.6 m/s
d. 73.3 m/s

24.    
  sec
m
26.28
1
4
3858.0
56.8
v
sec
kg
56.82020.0
4
630.13m
Avm
3858.0
9.2183h
80%x;KPa50P
kg
KJ
6.2920U
m
kg
630.13
kg
KJ
1.3214h
C400t;KPa4000PAt
2
2
2
3























π
π
ρ
ρ
ρ
79. Saturated liquid water enters an adiabatic steady-flow throttle valve at 500 kPa and leaves at 100 kPa. What is the
quality of the water liquid-vapor mixture leaving this valve?
a. 9.87%
b. 10.6%
c. 14.3%
d. 21.1%
80. Air enters the after burner nozzle of a jet fighter at 427°C with a velocity of 100 m/s. It leaves this adiabatic nozzle
at 377°C. Assuming that the air specific heats do not change with temperature, the velocity at the nozzle exit is:
a. 142 m/s
b. 178 m/s
c. 227 m/s
d. 332 m/s
sec
m
34.332v
sec
m
v)TT(C2000v
)TT(C
2000
VV
hΔKEΔ
00KEΔhΔ0
WPEΔKEΔhΔQ
2
2
121p2
12p
2
1
2
2







81. Air is compressed from 100 KPa, 300 K to 500 KPa, 500 K in a steady state, steady-flow compressor. Determine
the work required for this compressor per kg:
a. -132 kJ/kg
b. -181 kJ/kg
c. -203 kJ/kg
d. -241 kJ/kg
kg
KJ
8.180
n1
)TT(nmR
W
46.1n
P
P
T
T
K500T;KPa500P
K300T;KPa100P
12
n
1n
1
2
1
2
22
11
















25. kg514.1)65.2(57143.0m
m
m
x
%143.57)857.42100(x
%857.42100%x
22.4
0.60(16)
x
M
My
x
mmm
kg65.2
)27335(371.0
)3(101
m
mRTPV
K-kg
KJ
371.0
4.22
3143.8
R
4.220.40(32)0.60(16)M
Condition1st
2
2
2
2
4
42
O
O
O
O
CH
ii
i
CHO












KPa28.121P
)3(24
)27335)(3143.8(41.3
V
mRT
P
kg76.065.241.3m
m65.2m
kg41.3
3333.0
136.1
m
m
m
x
%67.66)33.33100(x
%33.33100%x
24
0.50(16)
x
240.50(32)0.50(16)M
Condition2nd
kg136.11.514-2.65m
m
m
x
addedO
addedO
CH
CH
O
CH
CH
CH
CH
2
2
4
4
2
4
4
4
4












82. A 3 m3 drum contains a mixture at 101 KPa and 35C of 60% Methane (CH4) and 40% oxygen (O2) on a volumetric
basis. Determine the amount of oxygen that must be added at 35C to change the volumetric analysis to 50% of
each component. Determine also the new mixture pressure.
For
CH 4: M = 16; k = 1.321
O2: R = 32 ; k = 1.395
83. Air enter the nozzle as shown at a pressure of 2700 KPa at a velocity of 30 m/sec and with an enthalpy of 923
KJ/kg, and leaves with a pressure of 700 KPa and enthalpy of 660 KJ/kg. If the heat loss is 0.96 KJ/kg, find the exit
velocity in m/sec if the mass flow rate is 0.2 kg/sec.
a. 727
b. 635
c. 842
d. 574
sec
m
2.727v
00
2000
(30)-v
923)-(6600.96-
0zΔ0;WnozzleaFor
WPEΔKEΔhΔQ
2
22
2




84. A gaseous mixture composed of 25 kg of N2, 3.6 kg of H2, and 60 kg of CO2 is at 200 KPa, 50C. Find the respective
partial pressures and compute the volume of each component at its own partial pressure and 50C.
Given: mN2 = 25 kg ; mH2 = 3.6 kg ; mCO2 = 60 kg
m = 25 + 3.6 + 60 = 88.6 kg
xN2 = 0.282 ; xH2 = 0.041 ; xCO2 = 0.678
P = 200 KPa ; T = 323 K
335.0y
446.0y
219.0y
046.0
44
678.
2
041.
28
282.0
Mi
xi
Mi
xi
Mi
xi
yi
2
2
2
CO
H
N






P
Pi
yi 
PN2 = .219(200) = 43.8 KPa
PH2 = .446(200) = 89.2 KPa
PCO2 = 0.335(200) = 67 KPa

26. 3
CO
3
H
3
N
iiiii
m67.54
67
)323)(189.0(60
V
m23.54
2.89
)323)(16.4(6.3
V
m76.54
8.43
)323(297.0(25
V
TRmVP
2
2
2




85. A centrifugal pump compresses 3000 L/min of water from 98 KPa to 300 KPa. The inlet and outlet temperatures are
25C (d = 994.36 kg/m3). The inlet and discharge piping are on the same level, but the diameter of the inlet piping
is 15 cm whereas that of the discharge piping is 10 cm. Determine the pump work in Kilowatts.
KW48)218.8(22.0W
sec
kg
218.8)36.994(05.0m
kg
KJ
0.22W
W0
2000
)83.2()4.6(
36.994
98300
00
WPEKE)P(UQ
sec
m
6.4
(0.10)
0.05(4)
v
sec
m
2.83
(0.15)
0.05(4)
v
sec
m
0.05
)60(1000
000,3
Q
22
22
21
3












ΔΔυΔΔ
π
π
86. A closed gaseous system undergoes a reversible process in which 30 KJ of heat are rejected and the volume
changes 0.14 m3 to 0.55 m3. The pressure is constant at 150 KPa. Determine the change of internal energy U and
the work done W.
KJ-91.5UΔ
61.5UΔ30-
KJ61.5)14.055.0(150)VV(PW
WUΔQ
12




87. Air in a piston cylinder occupies 0.12 m3 at 552 KPa. the air expands in reversible adiabatic process in which
PV1.4 = C, doing work on the piston until the volume is 0.24 m3. Determine
a) the work of the system
b) the net work if the atmospheric pressure is 101 KPa
KJ28.0812.12-40.2w
KJ12.120.12)-101(0.24W
KJ2.40
k-1
VPVP
W
KPa209P
(0.24)P552(0.12)
CPV:ocessPr
net
a
1122
2
1.4
2
1.4
k









27. KJ24.13Q
K-kg
KJ
0045.1
1-k
Rk
C
)T-(TmCQ
K4.478T
mR
W
T
kg07.0
RT
VP
m
mRTVP
)TT(mR)VV(PW
p
12p
12
1
11
111
1212







KPa28.368P
1
273))(150.31(4.125
P
kg31.006.025.0m
m10.50.5V
statemequilibriuAt
kg06.0
)303(125.4
150(0.5)
m
kg25.0
)293(125.4
)5.0(600
m
RT
PV
m
3
B
A








KJ533.6W
3.11
)03.0(150)2.0(74.12
n1
VPVP
PdVW
KPa74.12P
2.0
03.0
150
V
V
P
V
VP
P
n1
VPVP
PdVW
nintegratioBy
V
C
P
dVPW
systemClosedaFor
CVPVP
CPV
11222
1
2
3.1n
2
1
1n
2
n
11
2
11222
1
n
n
22
n
11
n































88. A piston cylinder contains air at 600 KPa, 290 K and a volume of 0.01 m3. A constant pressure process gives 54 KJ
of work out. Determine the heat transfer of the process.
Given:
P1 = P2 = 600 KPa
T1 = 290 K
V1 = 0.01 m3
W = 54 KJ (work out)
89. A 0.5 m3 rigid tank containing hydrogen at 20C and 600 KPa is connected by a valve to another 0.5 m3 rigid tank
that holds hydrogen at 30C and 150 KPa. Now the valve is opened and the system is allowed to reach thermal
equilibrium with surroundings which are at 15C. Determine the final pressure. Assume hydrogen as an ideal gas.
(For hydrogen R = 4.125 KJ/kg-K)
Given:
Tank A
VA = 0.5 m3
TA1 = 20 + 273 = 293 K
PA1 = 600 KPa
Tank B
VB = 0.5 m3
TB1 = 30 + 273 = 303 K
PB1 = 150 KPa
90. During some actual expansion and compression processes in piston cylinder devices, the gases have been
observed to satisfy the relationship PVn = C, where n and C are constants. Calculate the work done when a gas
expands from a state of 150 KPa and 0.03 m3 to a final volume of 0.2 m3 for the case of n = 1.3. Also show the
process on the PV diagram.
Given:
P1 = 150 KPa ; V1= 0.03 m3
V2 = 0.2 m3

28. 91. Five kg of methane gas is fed to a cylinder having a volume of 20 m3 and initially containing 25 kg of methane at
a pressure of 10 bar. Determine the specific volume, in m3/kg, of the methane in the cylinder initially. Repeat for the
methane in the cylinder after the 5 kg has been added. (For Methane: R = 0.5183 KJ/kg-K; k = 1.321)
m1 = 25 kg ; V1 = 20 m3 ; P1 = 10 Bar = 1000 KPa
m2 = 25 + 5 = 30 kg
/kgm66.0
525
20
2m
2V
2
K5.1543
)5183.0(25
)20(1000
Rm
VP
T
/kgm8.0
25
20
m
V
RTmVP
3
1
11
1
3
1
1
1
1111






υ
υ
92. A vessel of volume 0.2 m3 contains nitrogen at 101.3 KPa and 15ºC. If 0.2 kg of nitrogen is now pumped into the
vessel, calculate the new pressure when the vessel has returned to its initial temperature. For nitrogen: M = 28 and
k = 1.399. (187 KPa)
KPa187
2.0
)27315)(297.0(437.0
P
kg437.02.0237.0m
kg237.0
)27315(297.0
)2.0(3.101
m
mRTPV
297.0
28
3143.8
R
Final
Final









93. A certain perfect gas of mass 0.01 kg occupies a volume of 0.003 m3 at a pressure of 700 KPa and a temperature
of 131ºC. The gas is allowed to expand until the pressure is 100 KPa and the final volume is 0.02 m3. Calculate:
a) the molecular weight of the gas (16)
b) the final temperature (111.5ºC)
C6.111273
)520.0(01.0
)02.0(100
t
16
520.0
3143.8
M
52.0
)273131(01.0
)003.0(700
R
mRTPV






94. A perfect gas has a molecular weight of 26 kg/kgmol and a value of k = 1.26. Calculate the heat rejected
a) when 1 kg of the gas in contained in a rigid vessel at 300 KPa and 315ºC, and is then cooled until the pressure
falls to 150 KPa. (-361 KJ)
(rejected)KJ2.361Q
)588294(23.1(1)TT(mCQ
294
300
)588(150
T
T
P
T
P
CVAt
588273315T
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b) when 1 kg/sec mass flow rate of the gas enter a pipeline at 280ºC and flows steadily to the end of the
pipe where the temperature is 20ºC. Neglect changes in kinetic and potential energies.(-403 KW)

29. KW403.2280)-1.550)(20(1hΔQ
K-kg
KJ
1.550
1k
Rk
C
K-kg
KJ
0.320
26
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Rk
C
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93. The mass analysis of hydrocarbon fuel A is 88.5% Carbon and 11.5% Hydrogen. Another hydrocarbon fuel B
requires 6% more air than fuel A for complete combustion. Calculate the mass analysis of Fuel B.
Solution:
Fuel A: C = 0.885 ; H = 0.115
Fuel B: C = ; H =
(A/F)B = 1.06(A/F)A
(A/F)A = 11.44(0.885) + 34.32(0.115) = 14.0712 kg/kg
(A/F)B = 1.06(14.0712)= 14.9155 kg/kg
For fuel B: H + C = 1
H = (1 – C)
14.9155 = 11.44C + 34.32(1-C)
C = 84.8%
H = 15.2%
94. A diesel engine uses a hydrocarbon fuel represented by C12H26 and is burned with 30% excess air. The air and fuel
is supplied at 1 atm and 25C. Determine
a. the actual air-fuel Ratio
b. the m3 of CO2 formed per kg of fuel if the product temp. is 400C and a pressure of 1 atm.
c. The M and R of the Products
d. The M and R of the dry flue gas
Combustion with 100% theoretical air (basis 1 mole of fuel)
C12H26 + aO2 + a(3.76)N2  bCO2 + cH2O + a(3.76)N2
a = 18.5
b = 12
c = 13
Combustion with 30% excess air
C12H26 + 1.30aO2 + 1.30a(3.76)N2  bCO=+ cH2O + dO2 + 1.30a(3.76)N=
d = 5.55
nP = b + c + d + 1.3(18.5)(3.76) = 120.978
fuelofkg
airofkg
42.19
mn12
)m25.0n)(e1(28.137
a
F
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7.662
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COofm7.662
325.101
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V
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3
2
3
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983.29M
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978.107
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1
M
978.107cnn
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7.28M
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30. 95. The analysis of the natural gas showed the following percentages by volume: C2H6 = 9%; CH4 = 90%; CO2 = 0.2 %
and N2 = 0.8 %. Find the volume of air required per cu,m. of gas if the gas and air are at temperature of 16C and
a pressure of 101.6 KPa.
Solution: basis 100 moles of fuel)
9C2H6 + 90CH4 + 0.2CO2 + 0.8N2 + aO2 + a(3.76)N2  bCO2 + cH2O + dN2
By Carbon balance:
2(9) + 90 + 0.20 = b
b = 108.20
By Hydrogen Balance:
6(9) + 4(90) = 2c
c = 207
By O2 balance:
0.2 + a = 108.20 + (207/2)
a = 211.5
na = a(1 + 3.76)
nF = 100
na/nF = 10.07
96. Calculate the internal energy and enthalpy of 1 kg of air occupying 0.05 m3 2000 KPa. If the internal energy is
increased by 120 KJ as the air is compressed to 5000 KPa, calculate the new volume occupied by 1 kg of the air.
For air: R = 0.287 KJ/kg-ºK and k = 1.4.( 250.1 KJ/kg; 350.1 KJ/kg; 0.0296 m3)
1.350)4.348(0045.1h
1.250)4.348(7175.0U
K4.348
)287.0(1
)05.0(2000
T
mRTPV




97. When a certain perfect gas is heated at constant pressure from 15ºC to 95ºC, the heat required is 1136 KJ/kg.
When the same gas is heated at constant volume between the same temperatures the heat required is 808 KJ/kg.
Calculate Cp, Cv, k, and M of the gas. (14.2 KJ/kg; 10.1 KJ/kg; 1.405; 4.1 and 2.208)
98. A quantity of a certain perfect gas is compressed from an initial state of 0.085 m3, 100 KPa to a final state of 0.034
m3, 390 KPa. the Cv = 0.724 KJ/kg-ºC and Cp = 1.020 KJ/kg-ºC. The observed temperature rise is 146ºK. Calculate
R, the mass present, and U of the gas.(0.296 KJ/kg-K; 0.11 kg; 11.63 KJ)
99. A mass of 0.05 kg of air is heated at constant pressure of 200 KPa until the volume occupied is 0.0658 m3. Calculate
the heat supplied, the work and the change in entropy for the process if the initial temperature is 130ºC. (Q = 25.83
KJ; W = 7.38 KJ)
100. A 1 kg of nitrogen is compressed reversibly and isothermally from 101 KPa, 20ºC to 420 KPa. Calculate the
nonflow work and the heat flow during the process assuming nitrogen to be a perfect gas. ( Q = W = 124 kJ/KG)
101. Air at 102 KPa, 22ºC, initially occupying a cylinder volume of 0.015 m3 is compressed isentropically by a piston
to a pressure of 680 KPa. Calculate the final temperature, the final volume, the work done on the mass of air in the
cylinder. (234.3 ºC; .00387 m3; 2.76 KJ)
102. 1 kg of air is compressed from 110 KPa, 27 ºC in a polytropic process where n = 1.3 until the final pressure is
660 KPa. Calculate:
a) ∫PdV
b) - ∫VdP
c) S
103. There are 1.36 kg of air at 138 KPa stirred with internal paddles in an insulated rigid container, whose volume is
0.142 m3until the pressure becomes 689.5 KPa. Determine the work input and PV. ( 196.2 KJ; 78.3 KJ)
104. During an isentropic process of 1.36 kg/sec of air, the temperature increases from 4.44ºC to 115.6 ºC. for a
nonflow process and for a steady flow process (KE = 0 and PE = 0) Find:
a) U in KW
b) H in KW
c) W in KW
d) S in KW/ºK
e) Q in KW

31. 105. A certain perfect gas is compressed reversibly from 100 KPa, 17 ºC to a pressure of 500 KPa in a perfectly thermally
insulated cylinder, the final temperature being 77 ºC. The work done on the gas during the compression is 45
KJ/kg. Calculate, k , Cv, R and M of the gas.( 1.132; 0.75 KJ/kg-ºK; 0.099 KJ/kg-ºK; 84)
106. 1 kg of air at 102 KPa, 20 ºC is compressed reversibly according to a law PV1.3 = C to a pressure of 550 KPa.
Calculate the work done on the air and the heat supplied during the compression. (133.46 KJ/kg; -33.3 KJ/kg)
107. Oxygen (M = 32) is compressed polytropically in a cylinder from 105 KPa, 15ºC to 420 KPa in such a way that one
third of the work input is rejected as heat to the cylinder walls. Calculate the final temperature of the oxygen.
Assume oxygen to be perfect gas and take Cv = 0.649 KJ/kg-K. (113 ºC)
108. Air at 690 KPa, 260ºC is throttled to 550 KPa before expanding through the nozzle to a pressure of 110 KPa.
Assuming that the air flows reversibly in steady flow through the nozzle and that no heat is rejected, calculate the
velocity of the air at exit from the nozzle when the inlet velocity is 100 m/sec. ( 636 m/sec)
109. Air at 40ºC enters a mixing chamber at a rate of 225 kg/sec where it mixes with air at 15ºC entering at a rate of
540 kg/sec. Calculate The temperature of the air leaving the chamber, assuming steady flow conditions. Assume
that the heat loss is negligible. (22.4ºC)
A heat engine has a thermal efficiency of 45%. How much power does the engine produce when heat is transferred into
it at a rate of 109 kJ/Hr?
A) 50 MW
B) 75 MW
C) 100 MW
D) 125 MW
A refrigerator has a coefficient of performance of 1.6. How much work must be supplied to this refrigerator for it to reject
1000 kJ of heat?
A) 385 kJ
B) 627 kJ
C) 836 kJ
D) 1000 kJ
The thermodynamic efficiency of a heat engine that rejects heat at a rate of 20 MW when heat is supplied to it at a rate
of 60 MW is:
A) 33.3%
B) 50%
C) 66.7%
D) 75%
A Carnot engine operates using a 527 °C energy reservoir and a 27 °C energy reservoir. The thermodynamic efficiency
of this engine is:
A) 50%
B) 62.5%
C) 73.6%
D) 103%
A Carnot heat pump uses thermal reservoirs at -27 °C and 57 °C. How much power does this pump consume to produce
a 100 kW heating effect?
A) 9.1 kW
B) 12.7 kW
C) 15.3 kW

32. D) 20.7 kW
Saturated water vapor at 150 kPa is condensed to saturated liquid in a steady-flow, isobaric heat exchanger. The
released heat is transferred to the surrounding air whose temperature is 20 °C. The increase of the entropy associated
with this process is:
A) -4.731 kJ/kg-K
B) -2.366 kJ/kg-K
C) 2.366 kJ/kg-K
D) 4.731 kJ/kg-K
Steam at 2 MPa, 300 °C is expanded in a steady-flow, adiabatic turbine to 30 kPa. What is the lowest possible
temperature at the outlet of this turbine?
A) 69.1 °C
B) 101.1 °C
C) 150.7 °C
D) 203.2 °C
Steam at 2 MPa, 300 °C is expanded through a steady-flow, adiabatic turbine to 30 kPa. How much work does this
turbine produce?
A) 478.7 kJ/kg
B) 523.2 kJ/kg
C) 639.2 kJ/kg
D) 741.6 kJ/kg
Air at 5 MPa, 967 °C is expanded through a steady-flow device to 100 kPa, 27 °C. What is the change in the specific
entropy of the air?
A) -1.372 kJ/kg-K
B) -0.269 kJ/kg-K
C) 1.742 kJ/kg-K
D) 2.638 kJ/kg-K
A 0.5-kg steel (C = 0.5 kJ/kg-k) rivet cools from 800 K to 300 K upon being installed in a riveted building structure. The
entropy change of this rivet is:
A) -0.631 kJ/K
B) -0.245 kJ/K
C) 0.245kJ/K
D) 0.631 kJ/K
Oxygen at 100 kPa, 27 °C is compressed to 1 MPa in an adiabatic compressor whose isentropic efficiency is 0.80. The
oxygen temperature at the compressor outlet is:
A) 376 K
B) 421 K
C) 566 K
D) 649 K
Water undergoes the reversible process illustrated here as it passes through a steady-flow device that has one outlet
and one outlet. How much work does this device produce?
A) 0 kJ/kg
B) P (v2 - v1) kJ/kg
C) R (T2 - T1) kJ/kg
D) cv (T2 - T1) kJ/kg
Air is expanded in a closed system from 1 MPa, 327 °C to 100 kPa in an isentropic process. The system surroundings
are at 100 kPa, 27 °C. How much useful work did this system produce during this process?
A) 91 kJ/kg

33. B) 103 kJ/kg
C) 135 kJ/kg
D) 210 kJ/kg
A 1 m3 vessel contains air at 1 MPa, 327 °C. Assuming standard conditions for the surroundings, what is the maximum
amount of work that can be done by the air in this vessel?
A) 790 kJ
B) 826 kJ
C) 1012 kJ
D) 1290 kJ
Steam enters a turbine at 3 MPa, 350 °C with a velocity of 15 m/s. What is the specific exergy of this steam assuming
the surroundings are at standard conditions?
A) 678 kJ/kg
B) 827 kJ/kg
C) 968 kJ/kg
D) 1116 kJ/kg
Steam at 3 MPa, 350 °C is expanded through an adiabatic, steady-flow turbine to a saturated vapor at 100 kPa. The
second law efficiency of this turbine is:
A) 48.2%
B) 63.7%
C) 70.7%
D) 82.1%
A heat exchanger maintains the air temperature in a room at 25 °C by condensing saturated water vapor at 125 kPa to
saturated liquid water. The specific exergy destruction associated with this heat exchanger is:
A) 932 kJ/kg
B) 958 kJ/kg
C) 1241 kJ/kg
D) 1378 kJ/kg
Air is compressed from 100 kPa, 27 °C to 900 kPa, 327 °C in an adiabatic piston-cylinder device. What is the
irreversibility of this process?
A) 19.66 kJ/kg
B) 22.31 kJ/kg
C) 28.73 kJ/kg
D) 32.17 kJ/kg
An adiabatic, steady-flow heat exchanger condenses 10,000 kg/hr of saturated steam vapor at 200 kPa to a saturated
liquid also at 200 kPa. The condensing steam heats 220,000 kg/hr of air at 100 kPa, 25 °C to 100 kPa, 125 °C. What is
the rate at which exergy is destroyed by this heat exchanger?
A) 0 MJ/hr
B) 270 MJ/hr
C) 1327 MJ/hr
D) 2295 MJ/hr
A Carnot vapor power cycle operates its boiler at 3.0 MPa and its condenser at 50 kPa. What is the thermal efficiency
of this cycle?
A) 20%
B) 30%
C) 40%
D) 50%
A simple Rankine cycle operates the boiler at 3 MPa with an outlet temperature of 350 °C and the condenser at 50 kPa.
Assuming ideal operation and processes, what is the thermal efficiency of this cycle?
A) 7.7%
B) 17.7%
C) 27.7%

34. D) 37.7%
A simple Rankine cycle operates its boiler at 3 MPa with an outlet temperature of 350 °C and its condenser at 50 kPa.
The turbine has an isentropic efficiency of 0.9 while all other operating conditions and process are ideal. What is the
thermal efficiency of this cycle?
A) 25.0%
B) 30.9%
C) 35.9%
D) 40.9%
A simple, ideal Rankine cycle operates the boiler at 3 MPa and the condenser at 50 kPa. The temperature at the boiler
outlet is 400 °C. What is the rate at which heat must be supplied to the water in the boiler for a power production of 100
MW?
A) 157 MW
B) 218 MW
C) 273 MW
D) 352 MW
An ideal Rankine cycle with reheat operates the boiler at 3 MPa, the reheater at 1 MPa, and the condenser at 50 kPa.
The temperature at the boiler and reheater outlets is 350 °C. What is the thermal efficiency of this cycle?
A) 24.5%
B) 26.5%
C) 28.5%
D) 30.5%
An ideal Rankine cycle with reheat operates the boiler at 3 MPa, the reheater at 1 MPa, and the condenser at 50 kPa.
The temperature at the boiler and reheater outlets is 350 °C. The boiler and reheater are fired with a fuel that releases
9,000 kJ/kg of heat as it is burned. What is the mass flow rate of the fuel for such a cycle when sized to produce 50 MW
of net work?
A) 40 Mg/hr
B) 50 Mg/hr
C) 60 Mg/hr
D) 70 Mg/hr
An ideal Rankine cycle with an open-feedwater-heater regenerator operates the boiler at 3 MPa, the regenerator at 125
kPa, and the condenser at 50 kPa. At the boiler outlet, the temperature is 350 °C. What percentage of the mass flow
rate passing through the boiler is bled from the turbine for the regenerator?
A) 4.85%
B) 7.31%
C) 10.6%
D) 13.2%
An ideal Rankine cycle with an open-feedwater-heater regenerator operates the boiler at 3 MPa, the regenerator at 125
kPa, and the condenser at 50 kPa. At the boiler outlet, the temperature is 350 °C. What is the thermal efficiency of this
cycle?
A) 24.6%
B) 28.6%
C) 32.6%
D) 36.6%
A simple Rankine cycle operates the boiler at 3 MPa and the condenser at 50 kPa. The temperature at the boiler outlet
is 350 °C. The energy source is at 400 °C and the energy sink is at 27 °C. What is the irreversibility of this cycle per unit
of mass passing through the boiler?
A) 561.2 kJ/kg
B) 613.4 kJ/kg
C) 694.2 kJ/kg
D) 767.8 kJ/kg

35. A simple Rankine cycle produces 40 MW of power, 50 MW of process heat and rejects 60 MW of heat to the
surroundings. What is the utilization factor of this cogeneration cycle neglecting the pump work?
A) 50%
B) 60%
C) 70%
D) 80%
A basic R-134a, ideal vapor-compression refrigerator operates its evaporator at -16 °C and its evaporator at 1.4 MPa.
How much power will the compressor require to service a 10 kW cooling load?
A) 4.03 kW
B) 5.97 kW
C) 7.32 kW
D) 10.0 kW
A basic R-134a, ideal vapor-compression refrigerator operates its evaporator at 157 kPa and its evaporator at 1.4 MPa.
What is the rate at which the condenser rejects heat when this refrigerator services a 100 kW load?
A) 80 kW
B) 103 kW
C) 120 kW
D) 141 kW
An ideal R-134a vapor-compression heat pump operates its evaporator at 1.4 MPa and its condenser at -16 °C. The
coefficient of performance of this heat pump is:
A) 2.48
B) 2.79
C) 3.43
D) 3.79
A R-134a vapor-compression refrigerator operates its evaporator at 1.4 MPa and its condenser at 157 kPa. All the cycle
states and processes are ideal except for the compressor, which has an isentropic efficiency of 79%. How much power
must be supplied to the compressor when this refrigerator serves a100 kW cooling load?
A) 27.3 kW
B) 34.2 kW
C) 52.0 kW
D) 100 kW
A simple R-134a vapor-compression refrigerator system operates its evaporator at 157 kPa and the exit of the
compressor at 1.4 MPa. The working fluid enters the throttle valve as a saturated liquid at 1.2 MPa as a result of pressure
losses in the condenser and connection lines. What is the coefficient of performance of this device?
A) 2.64
B) 2.93
C) 3.26
D) 3.69
An ideal R-134a, dual compressor vapor-compression refrigerator system uses a flash chamber to separate the vapor
in the evaporator feed line. This system operates the evaporator at 133 kPa, the flash chamber at 400 kPa, and the
condenser at 1.4 MPa. What fraction of the mass flow rate passing through the evaporator passes through the
condenser?
A) 0.80
B) 1.00
C) 1.20
D) 1.50
An ideal R-134a, dual compressor vapor-compression refrigerator system uses a flash chamber to separate the vapor
in the evaporator feed line. This system operates the evaporator at 133 kPa, the flash chamber at 400 kPa, and the
condenser at 1.4 MPa. What is the coefficient of performance of this device?
A) 1.87
B) 2.63

36. C) 2.95
D) 3.17
A simple, ideal reversible Brayton cycle uses air as the working fluid and has a pressure ratio of 6. What is the refrigerato r
COP of this cycle when the temperature at the compressor entrance is -13 °C and that at the turbine entrance is 37 °C?
A) 0.33
B) 0.72
C) 1.48
D) 1.97
The composition of a mixture of nitrogen and carbon dioxide gases is 30%-N2 and 70%-CO2 by mole fraction. What is
the mass fraction of the nitrogen constituent?
A) 15.2%
B) 21.4%
C) 30.2%
D) 63.7%
A mixture of helium and nitrogen is 50%-He and 50%-N2 by mass analysis. What is the mole fraction of the helium in
this mixture?
A) 39.7%
B) 43.2%
C) 67.2%
D) 87.5%
The composition of a gas mixture is 40%-O2, 40%-N2, and 20%-He by mass analysis. What is the apparent molecular
weight of this mixture?
A) 6.71 kg/kg-mol
B) 13.02 kg/kg-mol
C) 15.70 kg/kg-mol
D) 18.60 kg/kg-mol
The composition of a mixture of gases is 50%-CO2, 40%-O2, and 10%-He by volume analysis. What is the apparent
molecular weight of this mixture?
A) 19.3 kg/kg-mol
B) 24.6 kg/kg-mol
C) 28.7 kg/kg-mol
D) 35.2 kg/kg-mol
A 1 m3 container contains a mixture of gases composed of 0.02 kg-mol of O2 and 0.04 kg-mol of He at a pressure of
200 kPa. What is the temperature of this ideal gas mixture?
A) 300 K
B) 350 K
C) 400 K
D) 450 K
A 200 liter container holds 0.5 kg of air and 0.2 kg of helium at a temperature of 350 K. What is the pressure of this ideal
gas mixture?
A) 1.4 MPa
B) 1.6 MPa
C) 1.8 MPa
D) 2.0 MPa
A mixture composed of 70%-CO2 and 30%-He by volume analysis is contained at 1 MPa. What is the partial pressure
of the He in this mixture?
A) 300 kPa
B) 450 kPa
C) 600 kPa

37. D) 700 kPa
A mixture of 30%-Ar and 70%-CO2 by volume analysis. This mixture is contained in a rigid vessel at 200 kPa, 27 °C.
The vessel is now heated until the mixture temperature is 127 °C. Assuming that the specific heats do not change, how
much heat was required?
A) 1.10 MJ/kg-mol
B) 2.40 MJ/kg-mol
C) 1.10 MJ/kg
D) 2.40 MJ/kg
A mixture consists of 30%-Ar and 70%-CO2 by volume analysis. This mixture is contained in a rigid vessel at 200 kPa,
27 oC. The vessel is now heated until the mixture temperature is 127 oC. Assuming constant specific heats, what is the
change in the entropy of the mixture?
A) 4.780 kJ/kg-mol-K
B) 6.900 kJ/kg-mol-K
C) 4.780 kJ/kg-mol-K
D) 6.900 kJ/kg-mol-K
A mixture of 20%-CO2 and 80%-N2 by volume is expanded from 1 MPa, 227 °C to 200 kPa as it passes through an
adiabatic, steady-flow turbine. Assuming this process is reversible and the specific heats are constant, how much work
is produced by this expansion?
A) 137.9 kJ/kg
B) 164.5 kJ/kg
C) 174.3 kJ/kg
D) 194.2 kJ/kg
What is the specific humidity of air at 150 kPa whose dry bulb temperature is 20 °C and relative humidity is 70%?
A) 0.000981 kg-wv/kg-da
B) 0.00382 kg-wv/kg-da
C) 0.00514 kg-wv/kg-da
D) 0.00686 kg-wv/kg-da
Using saturated liquid water and 0 °C as the reference state, what is the specific enthalpy of humid air at 120 kPa, 20
°C, and 50% relative humidity?
A) 32.71 kJ/kg-da
B) 35.63 kJ/kg-da
C) 38.93 kJ/kg-da
D) 41.72 kJ/kg-da
What is the dew-point temperature of humid air at 200 kPa, 30 °C, and 55% relative humidity?
A) 10 °C
B) 15 °C
C) 20 °C
D) 25 °C
Humid air at 150 kPa, 30 °C, and 80% relative humidity undergoes an isobaric cooling process until its temperature is
25 °C. Will any liquid condensate form during this process?
A) Yes
B) No
C) Not applicable
D) Not applicable
Humid air is cooled, dehumidified and reheated during an isobaric process. Which one of the psychometric charts below
correctly depicts these processes?
A) a
B) b
C) c
D) d

38. One-hundred cubic meters per minute of humid air at 101 kPa, 35 °C, 40% relative humidity is cooled to 25 °C in a
constant pressure process. The cooling rate for this process is:
A) 9.3 kW
B) 17.8 kW
C) 20.2 kW
D) 22.3 kW
Saturated humid air at 101 kPa, 20 °C is heated to 35 °C during an isobaric process. What is the final relative humidity
of this air?
A) 42%
B) 53%
C) 68%
D) 75%
Humid air at 101 kPa, 35 °C, 80% relative humidity is conditioned to 101 kPa, 25 °C, 50% relative humidity. How much
condensate is formed during this process?
A) 0.0087 kg/kg-da
B) 0.0168 kg/kg-da
C) 0.0193 kg/kg-da
D) 0.0231 kg/kg-da
Humid air at 101 kPa, 35 °C, 80% relative humidity is conditioned to 101 kPa, 25 °C, 50% relative humidity. How much
heat must be removed to accomplish this when the condensate leaves the system at 25 °C?
A) 41.7 kJ/kg-da
B) 46.7 kJ/kg-da
C) 52.3 kJ/kg-da
D) 57.5 kJ/kg-da
A standard atmospheric pressure cooling tower uses humid air at 30 °C, 60% relative humidity to cool liquid water from
55 °C to 40 °C. Saturated humid air leaves this tower at 35 °C. How much make-up water must be supplied to this
tower?
A) 0.0206 kg/kg-da
B) 0.0313 kg/kg-da
C) 0.0347 kg/kg-da
D) 0.0404 kg/kg-da
Five kilogram-mol of octane are burned with a stiochiometric amount of air. How much water is formed in the products
if the combustion is complete?
A) 15 kg-mol
B) 25 kg-mol
C) 35 kg-mol
D) 45 kg-mol
Methyl alcohol is burned with 30% excess air. How much unburned oxygen will there be in the products if the combustion
is complete?
A) 0.35 kg-mol-o2/kg-mol-fuel
B) 0.45 kg-mol-o2/kg-mol-fuel
C) 0.55 kg-mol-o2/kg-mol-fuel
D) 0.65 kg-mol-o2/kg-mol-fuel
Gaseous methane fuel is burned with 100% excess air. This combustion is incomplete with 10% of the carbon in the
fuel forming CO. The products of combustion are at 100 kPa. What is the partial pressure of the CO in the products?
A) 0.51 kPa
B) 1.36 kPa
C) 2.78 kPa
D) 10.5 kPa
Gaseous methane fuel is burned with 50% excess air. When the temperature of the products is 30 °C and the pressure
is 100 kPa, what fraction of the water in the products is liquid?
A) 31%

39. B) 48%
C) 62%
D) 74%
Dodecane is burned at constant pressure with 150% excess air. What is the air-fuel ratio for this process?
A) 37.5
B) 42.3
C) 48.7
D) 51.3
Liquid octane fuel is burned in an isobaric, steady-flow burner with 80% excess air. The air and fuel enter the burner at
25 °C and the combustion products leave at 427 °C. How much heat is released by this burner when the combustion is
complete?
A) 18,530 kJ/kg-fuel
B) 31,800 kJ/kg-fuel
C) 38,460 kJ/kg-fuel
D) 42,610 kJ/kg-fuel
One gallon of gasoline (octane) has a mass of 2.66 kg. What is the maximum amount of heat that can be produced
when one gallon of gasoline is burned with air?
A) 17,320 kJ/gal
B) 111,270 kJ/gal
C) 116,320 kJ/gal
D) 127,650 kJ/gal
In a metallurgical process, methane is burned at constant pressure, with a stiochiometric amount of air both of which
are at 25 °C. What is the maximum temperature of the products?
A) 1930 K
B) 2320 K
C) 2890 K
D) 3170 K
How irreversible is the combustion of methane at standard atmospheric pressure with 20% excess air when all reactants
and products are at 25 °C and the water in the products is all liquid?
A) 630,000 kJ/kg-mol-CH4
B) 780,200 kJ/kg-mol-CH4
C) 884,700 kJ/kg-mol-CH4
D) 1,110,000 kJ/kg-mol-CH4
What is the reversible work for CH4 burned with stiochiometric air when all products and reactants are at the standard
referance state?
A) 673,500 kJ/kg-mol-fuel
B) 718,300 kJ/kg-mol-fuel
C) 793,000 kJ/kg-mol-fuel
D) 817,900 kJ/kg-mol-fuel
At what temperature will 20% of carbon dioxide disassociate to carbon monoxide when the pressure is 0.1 atm?
A) 2240 K
B) 2420 K
C) 2690 K
D) 3120 K
Excess air is used in combustion reactions to control flame temperatures. Excess air will also _________________
when Dn is positive.
A) Produce more incomplete combustion
B) Produce more complete combustion
C) Produce undesirable combustion
D) Have no effect

40. A mixture of 1 kg-mol of CO and 1 kg-mol of O2 is heated to 3000 K at a pressure of 1 atm. What fraction of the original
CO becomes CO2?
A) 27.8%
B) 37.6%
C) 69.2%
D) 90.1%
Increasing the temperature of an ideal gas increases ________________.
A) The number of reactants in the products
B) The number of inert gases in the product
C) The number of disassociation products
D) None of these
A mixture consists of 1 kg-mol of CO, 1 kg-mol of O2, and 2 kg-mol of N2. Treating the nitrogen as an inert gas, how
much CO2 is formed when the temperature and pressure of this mixture is 2600 K and 1 atm?
A) 0.371 kg-mol
B) 0.615 kg-mol
C) 0.832
D) 0.957 kg-mol
A mixture of 1 kg-mol of CO2, 1 kg-mol of O2, and 2 kg-mol of N2 is heated to 4000 K at a pressure of 1 atm. Assuming
that the final mixture consists of CO2, CO, O2, O, and N2, how much atomic oxygen is present in the final mixture?
A) 0.33
B) 0.50
C) 0.67
D) 0.90
What is the approximate heat of reaction at 3400 K for the disassociation of CO2 to CO?
A) 5961 kJ/kg-mol
B) 7482 kJ/kg-mol
C) 8785 kJ/kg-mol
D) 9213 kJ/kg-mol
A system is composed of gasoline liquid and vapor, and air. According to Gibbs phase rule how many independent
properties are required for phase equilibrium?
A) 0
B) 1
C) 2
D) 3
When the water temperature of the Great Salt Lake is 20 °C, what is the mass fraction of the salt dissolved in the water?
A) 26.5%
B) 32.1%
C) 36.7%
D) 40.3%
The contents of a can of soft drink consists of CO2 dissolved in water and a vapor space filled with CO2 and H2O vapor.
At 17 oC and 2 atm, what is the mole fraction of the CO2 in the liquid mixture?
A) 0.00156
B) 0.00735
C) 0.0107
D) 0.0312
At one location in a nozzle, the air temperature is 400 K and the air velocity is 400 m/s. What is the stagnation enthalpy
(based on temperature dependent specific heats) of the air at this location?
A) 300 kJ/kg
B) 357 kJ/kg
C) 470 kJ/kg
D) 481 kJ/kg

41. At one location in a nozzle, the air temperature is 400 K and the air velocity is 450 m/s. What is the Mach number at this
location?
A) 0.97
B) 1.12
C) 1.37
D) 2.02
Air at 20 kPa flows with a Mach number of 1.5. What is the stagnation pressure of this air?
A) 22.2 kPa
B) 41.7 kPa
C) 56.2 kPa
D) 73.4 kPa
Air in a large tank at 350 K and 200 kPa is supplied to an isentropic converging-diverging nozzle. What is the temperature
at a point in this nozzle where the Mach number is 1.2?
A) 198 K
B) 271 K
C) 360 K
D) 395 K
An isentropic, converging-diverging nozzle operates with stagnation conditions 400 kPa, 500 K. This nozzle has a throat
area of 0.01 m2 and is chocked. What is the mass flow rate through this nozzle?
A) 5.01 kg/s
B) 7.23 kg/s
C) 8.32 kg/s
D) 9.81 kg/s
The exit of the diverging section of an isentropic nozzle has twice the area of the nozzle throat. What is the Mach number
at the exit when the exit flow is supersonic?
A) 1.80
B) 2.00
C) 2.20
D) 2.40
The exit of the diverging section of an isentropic nozzle has twice the area of the nozzle throat. If the stagnation pressure
at the throat is 200 kPa, what is the pressure at the nozzle exit when the exit flow is supersonic?
A) 18.7 kPa
B) 32.2 kPa
C) 87.3 kPa
D) 137.2 kPa
An aircraft flies through 80 kPa, 270 K still air with a Mach number of 1.30. A normal shock wave will form directly in
front of this aircraft. What is the stagnation pressure acting on this aircraft?
A) 61 kPa
B) 73 kPa
C) 101 kPa
D) 193 kPa
A normal shock wave forms in the diverging portion of a nozzle at a point where Mx = 1.5. The area at the exit of this
nozzle is 50% larger then that where the shock wave forms. What is the Mach number at the nozzle exit?
A) 1.2
B) 1.12
C) 0.38
D) 0.24
Steam at 3.0 MPa, 500 °C, and negligible velocity is expanded to 0.8 MPa through an isentropic nozzle. What is the
velocity of the steam at the nozzle exit?
A) 268 m/s
B) 522 m/s

42. C) 738 m/s
D) 894 m/s
b. A gaseous mixture has the following volumetric analysis O2, 30%; CO2, 40% N2, 30%. Determine
a) the analysis on a mass basis
b) the partial pressure of each component if the total pressure is 100 KPa and the temperature is 32C
c) the molecular weight and gas constant of the mixture
Gas yi M k Cp Cv R xi Pi Mixture
O2 0.30 32 1.395 0.918 0.658 0.260 0.27 30 M 35.6
CO2 0.40 44 1.288 0.845 0.656 189 0.494 40 R .234
N2 0.30 28 1.399 1.041 0.744 0.297 0.236 30 P 100
69. Consider 2 kg of CO and 1 kg of CH4 at 32C that are in a 0.6 m3 rigid drum. Find:
a) the mixture pressure P in KPa
b) the volumetric analysis
c) the partial pressures in KPa
d) the heat to cause a temperature rise of 50C.
70. A gaseous mixture has the following volumetric analysisO2, 30%; CO2, 40% N2, 30%. Determine
a) the analysis on a mass basis
b) the partial pressure of each component if the total pressure is 100 KPa and the temperature is 32C
c) the molecular weight and gas constant of the mixture
71. A gaseous mixture has the following analysis on a mass basis, CO2, 30%; SO2, 30%; He, 20% and N2, 20%.
For a total pressure and temperature of 101 KPa and 300 K, Determine
a) the volumetric or molal analysis
b) the component partial pressure
c) the mixture gas constant
d) the mixture specific heats
72. A cubical tank 1 m on a side, contains a mixture of 1.8 kg of nitrogen and 2.8 kg of an unknown gas. The
mixture pressure and temperature are 290 KPa and 340 K. Determine
a) Molecular weight and gas constant of the unknown gas
b) the volumetric analysis
73. A mixture of ideal gases at 30C and 200 KPa is composed of 0.20 kg CO2, 0.75 kg N2, and 0.05 kg He.
Determine the mixture volume.
74. In determining the specific heat of a new metal alloy,0.15 kg of the substance is heated to 400C and then
placed in a 0.2 kg aluminum calorimeter cup containing 0.4 kg of water at 10C. If the final temperature of the
mixture is 30.5C, what is the specific heat of the alloy.( ignore the calorimeter stirrer and thermometer)

43. CpAl = 0.92 KJ/kg-C; Cpw = 4.186 KJkg-C
75. An air compressor handles 8.5 m3/min of air with  = 1.26 kg/m3 and P = 101.325 KPa and it discharges at P =
445 KPag with  = 4.86 kg/m3. The U = 82 KJ/kg and the heat loss by cooling is 24 KJ/kg. Neglecting KE
and PE, find W in KJ/min.
76. A 0.1 kg of aluminum (Cp=0.92 KJ/kg-C) at 90C is immersed in 1 kg of water from 20C . Assuming no heat
is lost to the surroundings or container , what is the temperature of the metal and water when they reached
thermal equilibrium?
77. Water is flowing in a pipe with varying cross section area, and at all points the water completely fills the pipe. At
point 1 the cross section area of the pipe is 0.070 m2 and the velocity is 3.50 m/sec.
a. What is the fluid speed at points in the pipe where th cross section area is 0.105 m2 and 0.047 m2.
b. Calculate the volume of water discharged from the open end of the pipe in 1 hour.
78. A sealed tank containing sea water to a height of 11 m also contains air above the water at a gage pressure of
3 atmosphere. Water flows out from the bottom through a small hole. Calculate the efflux speed of the water.
79. A copper pot with a mass of 0.500 kg contains 0.170 kg of water at a temperature of 20C. A 0.250 kg block of
iron at 85C is dropped into the pot. Find the final temperature, assuming no heat loss to the surroundings.
Ccopper = 0.390 KJ/kg-C; Cwater = 4.19 KJ/kg-C and Ciron = 0.470 KJ/kg-C.
80. At one point in a pipeline the water speed is 3 m/sec and the gage pressure is 50 KPa. Find the gage pressure
at a second point in the line, 11 m lower than the first , if the pipe diameter at the second point is one half the
first.
81. A closed system containing a gas expands slowly in a piston cylinder in accordance to PV2 = C. If the initial
pressure is 500 KPa, initial volume is 50 L and the final pressure is 200 KPa, find the work done by the system.
82. A steam turbine receives superheated steam at 1.4 MPa and 400C (h = 3121 KJ/kg). The steam leaves the
turbine at 0.101 MPa and 100C (h = 2676 KJ/kg).The steam enters the turbine at 15 m/sec and exits at 60
m/sec. The elevation difference between entry and exit ports is negligible. The heat loss through the turbine
walls is 2 KW. Calculate the power output if the mass flow through the turbine is 0.5 kg/sec.
83. A small circular hole 6 mm in diameter is cut in the side of a large water tank 14 m below the water level in the
tank. The top of the tank is open to the atmosphere. Find the velocity of water exiting the hole and the volume
discharged per unit time.
84. Oxygen (M = 32) is compressed polytropically in a cylinder from 105 KPa, 15ºC to 420 KPa
The decrease in internal energy of 1.36 kg of an ideal gas is –342.9 KJ when the pressure decreases from
689.3 KPa to 137.86 KPa and the volume increases from 0.0425 m3 0.127 m3. Cv = 1.047 KJ/kg-K. Determine
the value of k.
85. The working fluid of a gas turbine passes through the machine at a steady rate of 10 kg/sec. It enters with a
velocity of 100 m/sec and specific enthalpy of 2000 KJ/kg and leaves at 50 m/sec with a specific enthalpy of
1500 KJ/kg. If the heat lost to surroundings as the fluid passes through the turbine is 40 KJ/kg, calculate the
power developed.
86. 0.07 m3 of gas at 4.14 MPa is expanded in an engine cylinder and the pressure at the end of expansion is
310 KPa. If the expansion is polytropic with PV1.35 = C, find the final volume.
87. Helium gas ( R=2.077 KJ/kg-K; k= 1.667) enters a steady state – steady flow expander at 800 KPa, 300C and
exits at 120 KPa. The mass flow rate is 0.2 kg/sec and the expansion process is PV1.3 = C. Calculate W of the
expander in KW.
88. A pressure gage at elevation 8 m on a side of a tank containing a liquid reads 57.4 KPa. Another gage at
elevation 5 m reads 80 KPa. Determine the density of the liquid.
89. Gas at a pressure of 95 KPa, volume 0.2 cu.m. and temperature 17C, is compressed until the pressure is
275 KPa and the volume is 0.085 cu.m.. Calculate the final temperature.
90. A liquid of density 800 kg/cu.m., specific heat of 2.5 KJ/kg-K and temperature of 27C is mixed with another
liquid of density 820 kg/cu.m., specific heat 1.9 KJ/kg-K and temperature of 55C in the ratio of one of the first
liquid to three of the second by volume. Find the resulting temperature.
91. A rigid container contains 1 mole of nitrogen gas that slowly receives 3 KCal of heat. What is the change in
internal energy of the gas in KJ.For N2: M = 28; K = 1.399
92. A certain perfect gas of mass 0.01 kg occupies a volume of 0.003 m3 at a pressure of 700 KPa and a temperature
of 131ºC. The gas is allowed to expand until the pressure is 100 KPa and the final volume is 0.02 m3. Calculate:
a) the molecular weight of the gas
b) the final temperature
93. A cubical tank 1 m on a side, contains a mixture of 1.8 kg of nitrogen (M = 28; k = 1.399) and 2.8 kg of an
unknown gas. The mixture pressure and temperature are 290 KPa and 340 K. Determine
a) Molecular weight and gas constant of the unknown gas

44. b) the volumetric analysis
94. A volume of gas having initial entropy of 5317.2 KJ/K is heated at constant temperature of 540C until the
entropy is 8165.7 KJ/K. How much heat is added and how much work is done during the process.
95. A 283 L drum contains a gaseous mixture at 690 KPa and 38C whose volumetric composition is 30% O2 and
70% CH4. How many kg of mixture must be bled and what mass of O2 added in order to produce at the original
pressure and temperature a mixture whose new volumetric composition is 70% O2 and 30% CH4.
For O2: M = 32 ; k = 1.395For CH4; M = 16 ; k = 1.321
100. A certain perfect gas of mass 0.01 kg occupies a volume of 0.003 m3 at a pressure of 700 KPa and a temperature
of 131ºC. The gas is allowed to expand until the pressure is 100 KPa and the final volume is 0.02 m3. Calculate:
a) the molecular weight of the gas
b) the final temperature
101. When a certain perfect gas is heated at constant pressure from 15ºC to 95ºC, the heat required is 1136 KJ/kg.
When the same gas is heated at constant volume between the same temperatures the heat required is 808
KJ/kg.
Calculate Cp, Cv, k, and M of the gas.
102. A closed vessel of 0.7 m3 internal volume contains a gas at 58 Kpa and 18C and with R = 0.27 KJ/kg-K.If now
0
0.35 kg of another gas at 18C and R = 0.29 KJ/kg-K is also admitted into the vessel. Calculate the final
pressure
of the mixture.
103. A closed system consisting of 2 kg of a gas undergoes a process during which the relationship between
pressure and specific volume is PV1.3 = C. The process begins with P1 = 1 bar, 1 = 0.5 m3/kg and ends with P2
=
0.25 bar. Determine the final volume, in m3, and plot the process on a graph of pressure versus specific volume.
104. Four kilograms of a certain gas is contained within a piston–cylinder assembly. The gas undergoes a process
for
which the pressure - volume relationship is PV1.5 = C. The initial pressure is 3 bar, the initial volume is 0.1 m3,
and
the final volume is 0.2 m3. The change in specific internal energy of the gas in the process is U = - 4.6 kJ/kg.
There are no significant changes in kinetic or potential energy. Determine the net heat transfer for the process,
in
kJ. (Q = -0.8 KJ)
105. Calculate the change of entropy per kg of air (R = 0.287 KJ/kg-K; k = 1.4) when heated from 300K to 600K
while
the pressure drops from 400 KPa to 300 KPa. (S = 0.78 KJ/kg-K)

45. 106. A 5 kg quantity of oxygen (M = 32; k = 1.395) is heated from 250 K to 400 K at constant pressure. Determine
a. h
b. U
c. S
d. W =  P dV
107. A 5 m3 tank contains chlorine (R = 0.1172 KJ/kg-K) at 300 KPa and 300K after 3 kg of chlorine has been used.
Determine the original mass and pressure if the original temperature was 315 K. (45.66 kg ; 337.15 KPa)
108. A gaseous mixture has the following volumetric analysis: O2 = 30%; CO2 = 40% ; N2 = 30%. Determine the
gravimetric analysis the partial pressure of each component if the total pressure is 100 KPa and the temperature
is 32C the molecular weight and gas constant of the mixture
For
O2: M = 32 ; k = 1.395
CO2: M = 44 ; k = 1.288
N2: M = 28 ; k = 1.399
109. How many kilograms of N2 must be mixed with 3.6 kg of CO2 in order to produce a gaseous mixture that is 50%
by volume of ach constituents.
110. For the resulting mixture, determine M and R, and the partial pressure of the N2 if that of the CO2 is 138 KPa.
111. The exhaust from a diesel engine using a high grade hydrocarbon fuel has an Orsat Analysis of, 10.2% CO2 ;
7.9% O2 and 81.9% N2.Determine
a. the value of n and m from CnHm
b. the ratio of H to C in the fuel by mass
c. the actual air fuel ratio
d. the theoretical air – fuel ratio
d the percent excess air
Given:
Orsat Analysis
CO2 = 10.2 %
O2 = 7.9 %
N2 = 81.9 %
Combustion Equation (Basis 100 moles of dry flue gas)
222222mn N9.81O9.7OyHCO2.10N)76.3(xxOHC 
By carbon, hydrogen, nitrogen and oxygen balance
n = 10.2 ; m = 14.73; x = 21.78 ; y = 7.36
1203.0
n12
m
Cofkg
Hofkg

fuelofkg
airofkg
80.21
73.14)2.10(12
)28)(76.3)(78.21()32(78.21
F
A
actual









22222mn N)76.3(aOcHbCON)76.3(aaOHC 
a = 13.9; b = 10.2 ; c = 7.37
fuelofkg
airofkg
9.13
73.14)2.10(12
)28)(76.3(9.13)32(9.13
F
A
ltheoretica


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
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%5757.0e
1
F
A
F
A
e
ltheoretica
actual
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112. A furnace burns natural gas that has the following volumetric analysis: CH4 = 90% ; C2H6 = 7% and C3H8 = 3%.
The gas fuel flow rate is 0.02 m3/sec and 25% excess air is required for complete combustion. The natural gas
and

46. air enter at 25C and 101 KPa. The exhaust gas (products) has a temperature of 1000C and 101 KPa.
Determine
the following
The combustion equation
The volumetric analysis of the products
The molecular weight M and gas constant R of the products
The density of the products in kg/m3
The orsat analysis of the products
The flue gas velocity exiting the smokestack if the stack diameter is 1 m
22222283624
22222283624
2222283624
N32.10O55.0OH13.2CO13.1N32.10O74.2HC03.0HC07.0CH9.0
55.0d
N)76.3(a)25.1(dOOcHbCON)76.3(a)25.1(aO)25.1(HC03.0HC07.0CH9.0
0.25eairexcesswithcombustion
13.2c
13.1b
2.2a
N)76.3(aOcHbCON)76.3(aaOHC03.0HC07.0CH9.0








Volumetric analysis
CO2 = 8%
H2O = 15.08%
O2 =3.88%
N2 = 73.04%
M = 27.93 kg/kgm
R = 0.298 KJ/kg-K
Orsat analysis
CO2 = 9.42%
O2 = 4.57%
N2 = 86%
113. A gas fired thermal power plant uses two types of hydrocarbon fuel with the following molal (volumetric analysis)
CH4 = 68% ; C2H6 = 32%. Fuel and air is supplied to the boiler at 101 KPa and 25C with 30% excess air
requirement for complete combustion. Product temperature and pressure are 1000C and 101 KPa,
respectively.
Determine the following:
a. the combustion equation
b. the theoretical and actual air fuel ratio
c. the Orsat analysis of the products
d. the molecular weight and gas constant of the products
e. the kg of CO2 formed per kg of fuel burned
f. the partial pressure of H2O in the products
Combustion with 100% theoretical air
0.68CH4 + 0.32C2H6 + 2.48O2 + 9.32N2 → 1.32 CO2 + 2.32 H2O + 9.32 N2
a = 2.48 ; b = 1.32 ; c = 2.32
Combustion with excess air e = 0.30
d = 0.74
0.68CH4 + 0.32C2H6 + 3.22O2 + 12.12N2 → 1.32 CO2 + 2.32 H2O + 0.74O2 + 12.12 N2
61.21
62.16



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




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
a
T
F
A
F
A
Orsat Analysis
CO2 = 9.3%
O2 = 5.24%

47. N2 = 85.45%
Molecular Weight and Gas Constant
M = 28.05
R = 0.296
Kg of CO2/kg of fuel =58.08/20.48 = 2.84 kg/kg
PH2O = 14.24 KPa
114. Air is contained in a cylinder fitted with a frictionless piston. Initially the cylinder contains 500 L of air at 150 KP a
and 20 C. The air is then compressed in a polytropic process ( PVn = C) until the final pressure is 600 KPa, at
which point the temperature is 120 C. Determine the work W and the heat transfer Q. (R = 0.287 KJ/kg-K ; k =
1.4)
Given:
V1 = 0.50 m3 ; P1 = 150 KPa ; T1 = 293 K
P2 = 600 KPa ; T2 = 393 K ;
Process: PVn = C
KJ951
T
T
n1
VP
W
WUQ
27.1n
P
P
ln
T
T
ln
n
1n
P
P
T
T
1
211
1
2
1
2
n
1n
1
2
1
2
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
115. A steam turbine of a coal fired thermal power plant receives steam at 7 MPa and 500C (h1 = 3410.3 KJ/kg ; S1 =
6.7975 KJ/kg-K) with a velocity of 30 m/sec and expands isentropically to the condenser at a pressure of 20 KPa
with a velocity of 90 m/sec. Calculate the ideal power developed by the turbine for a steam flow rate of 37.8 kg/sec
assuming PE in the turbine to be negligible.
At 20 KPa
Sf = 0.8320 KJ/kg-K ; Sg = 7.9085 KJ/kg-K ; Sfg = 7.0765 KJ/kg-K
hf = 251.4 KJ/kg ; hg = 2609.7 KJ/kg ; hfg = 2358.3 KJ/kg
SOLUTION:
6.7975 = O.8320 + x2(7.0765)
x2 = 0.839
h2 = 251.4 + (0.839)(2358.3) = 2230.014 KJ/kg
 
KW73.478,44W
)1000(2
)30()90(
)3.3410014.2230(8.37KEhmW
KE-h-W
0PEand0Q
WPEKEhQ
22
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


116. Air which is initially at 120 KPa and 320K occupies 0.11 m3. It is compressed isothermally until the volume is
halved and then compressed it at constant pressure until the volume decreases to ¼ of the initial volume. Sketch
the process on the PV and TS diagrams. Then determine the pressure, the volume and temperature in each state.
(For air: R = 0.287 KJ/kg-K ; k = 1.4)
Given:
P1 = 120 KPa ; T1 = 320K; V1 = 0.11 m3; T2 = 320K; V2 = ½V1; V3 = ¼V1
For air: R = 0.287 KJ/kg-K; k = 1.4
Processes:
KJ31Q
1-k
R
C
KJ64)T-(TmCU
kg892.0
RT
VP
m
v
12v
1
11





48. P
V
T
S
1
2
T = C
3
12
3
P = C
1 to 2: T = C
2 to 3: P = C
Solution:
At 1 to 2: T = C
P1V1 = P2V2
T1 = T2 = 320K
V2 = ½V1 = ½(0.11) = 0.055 m3
KPa240)2(120
V
V
PP
2
1
12 






At 2 to 3: P = C
P3 = P2 = 240 KPa
V3 = ¼V1 = ¼(0.11) = 0.0275 m3
K160
055.0
0275.0
320T
V
V
T
T
3
2
3
2
3









From
3
3
3
2
2
2
1
1
1
P
RT
P
RT
P
RT
P
RT




1 = 0.765 m3/kg
2 = 0.383 m3/kg
3 = 0.191 m3/kg
117. A cylinder fitted with a frictionless piston contains 5 kg of superheated water vapor at 1,000 KPa & 250C (h1 =
2942.6 KJ/kg ; U1 = 2709.9 KJ/kg ; S1 = 6.9247 KJ/kg-K). This system is now cooled at constant pressure until the
water reaches a quality x2 of 50%. Calculate the heat transferred and the work done during this process, and draw
the process on the PV & TS plane.
At 1000 KPa at saturation
hf = 762.81 KJ/kg; hg = 2778.1 KJ/kg; hf g = 2015.29 KJ/kg
Uf = 761.68 KJ/kg; Ug = 2583.6 KJ/kg ; Uf g = 1281.92 KJ/kg
Sf = 2.1387 KJ/kg-K; Sg = 6.5865 KJ/kg-K; Sf g = 4.4478 KJ/kg-K

49. KJ5.6756536.3-5860.8U-QW
KJ3.65362709.9)-5(1402.64)U-m(UU
KJ8.58602942.6)-5(1770.44)h-m(hQ
CPAt
KJ/kg1402.64)92.1281(50.068.761U
KJ/kg44.1770)26.2015)(50.0(81.762h
12
12
2
2






118. A small circular hole 6 mm in diameter is bored in the side of a large water tank 14 m below the water level in the
tank. The top of the tank is open to the atmosphere and the velocity on the water surface is negligible. Find the
velocity of water exiting the hole and the volume discharged in L/sec. (water = 1000 kg/m3)
L/sec47.0/secm10x7.4
4
)57.16()006.0(
m
m/sec57.16)2(9.81)(14v
0Z;0v
v)ZZ(g2v
1000
)ZZ(g
2000
vv
PEKE
0Q
0W
0P
0U
WPEKEPUQ
34-
2
2
11
2
1212
12
2
1
2
2















119. A piston cylinder device, whose piston is resting on a set stops, initially contains 3 kg of air at 200 KPa and 27C.
The mass of the piston is such that a pressure of 400 KPa is required to move it. Heat is now transferred to the air
until its volume doubles. Determine the work done by the air and the total heat transferred to the air during this
process. Also, show the process on a P-V diagram. (For air: R = 0.287 KJ/kg-K ; k = 1.4)
P
V
T
S
12
1
2
 1
 2
14 m
Q
P T
1
2 3
3
1
2
V =
C
P = C

50. KJ1808.1645.75Q
KJW
1.3)-400(2.6)V-P(VW
KJQ
600)-12003(1.0045)()T-(TmCQ
K
m
V
V
CPAt
KJ300)-6003(0.7175)(Q
K
P
P
VV
CV
T
23
p
23pp
3
2
3
v
1
2
21
85.2453
520
1.1808
1200T
600
T
3.1
6.2
6.2V2V
T
T
75.645
600T
T
T
At
3
3
13
2
3
2
1
2















120.
121. A closed system consisting of 2 kg of a gas undergoes a process during which the relationship between
pressure and specific volume is PV1.3 = constant. The process begins with P1 = 1 bar, 1 = 0.5 m3/kg and ends
with P2 = 0.25 bar. Determine the final volume, in m3, and plot the process on a graph of pressure versus
specific volume. (Note: 100 KPa = 1 Bar)
m = 2 kg
P1 = 1 Bar = 100 KPa ; P2 = 0.25 Bar = 25 KPa
1 = 0.5 m3/kg
Process: PV1.3 = C
3
22
3
3.1
1
2
3.1
1
2
1
1
2
3.1
22
3.1
11
m9.2)45.1(2mV
kg
m
45.1
25
100
5.0
P
P
PP


















122. Suppose that 42,200 KJ of heat energy are supplied in a small boiler to 25 kg of water at 90C. What part of the
water in kg will be vaporized, if the initial enthalpy of water is 376.78 KJ/kg and latent heat of vaporization (hf g)of
water is 2257 KJ/kg. Neglect changes in kinetic and potential energies.
vaportovaporizedwaterofmasskg23.18m
m
m
x
793.0x
(2257)x100(4.187)h
KJ/kg78.206478.376
25
200,42
h
)hh(mQ
v
v
2
2
22
2
12






123. Calculate the heat required to be given to 2 kg of ice at -15C to change into steam at atmospheric pressure, taking
the values
Freezing point temperature = 0C
Specific heat of ice = 2.04 KJ/kg-K

51. Latent heat of fusion = 335 KJ/kg
Specific heat of water = 4.2 KJ/kg-K
Latent heat of evaporation = 2256.7 KJ/kg
 
KJ6.6084Q
7.2256)0100(2.4335)150(04.2mQ


124. A liquid of density 800 kg/m3 specific heat of 2.5 KJ/kg-K and temperature of 27C is mixed with another liquid of
density 820 kg/m3, specific heat 1.9 KJ/kg-K and temperature of 55C in the ratio of one of the first liquid to three
of the second by volume. Find the resulting temperature.
Qh = Qc
mh(Cph)(55 - t) = mc(Cpc)(t – 27)
C6.46
)428.1
55.1155
t
55.11t428.0t55
)27t(428.0)t55(
)27t)(5.2)(800(V)t55)(9.1)(820(V3
Vm
Vm
Vm
m
V
V
m
3VV;
3
1
V
V
cc
hhh
ccc
ch
h
c













A 3 m diameter by 4.5 m height vertical tank is receiving water ( = 978 kg/m3) at the rate of 1.13 m3/min and is
discharging through a 150 mm  with a constant velocity of 1.5 m/sec. At a given instant, the tank is half full.
Find the water level and the mass change in the tank 15 minutes later.
Two gaseous streams containing the same fluid enter a mixing chamber and leave as a single stream. For the first
gas the entrance condition are: A1 = 500 cm2 ; v1 = 730 m/sec ; 1 = 1.60 kg/m3. For the second gas the entrance
condition are A2 = 400 cm2; m2 = 8.84 kg/sec ; 2 = .502 m3/kg. The exit stream conditions is: v3 = 130 m/sec
and 3 = 0.437 m3/kg.
Determine

52. (a) the total mass flow leaving the chamber
(b) the velocity of gas 2.
In determining the specific heat of a new metal alloy,0.15 kg of the substance is heated to 400C and then placed
in a 0.2 kg aluminum calorimeter cup containing 0.4 kg of water at 10C. If the final temperature of the mixture
is 30.5C , what is the specific heat of the alloy. (ignore the calorimeter stirrer and thermometer)
Cpal = 0.92 KJ/kg-C; Cpw = 4.187 KJkg-C
It is required to lift five people on an elevator a distance of 100 m. The work is found to be 341.2 KJ and g = 9.75
m/sec2. Determine the average mass per person.
Twenty kilograms of ice at -8C is placed in a 120 kgs of water at 40C. Assuming no heat lost to or absorbed from
the surroundings, what will be the resulting equilibrium temperature of the mixture.
Specific heat of ice = 2.22 KJ/kg-C
Specific heat of water = 4.19 KJ/kg-C
Freezing point temperature of water = 0C
hF of ice = 334.9 KJ/kg
A cup of coffee of volume 0.3 L is heated from a temperature of 25oC to 60oC at a pressure of 100 kPa. Determine the
change in the (a) internal energy, (b) enthalpy and (c) entropy. Assume the density and specific heat of coffee to be
1100 kg/m3 and 4.1 kJ/kg.K respectively. Employ the SL model. (d) What-if scenario: How would the answers change
if the heating was done inside a chamber pressurized at 1 MPa? [Manual Solution] [TEST Solution]
Answers: (a) 47.36 kJ (b) 47.36 kJ (c) 0.15 kJ/kg.K (d) No changes
A block of solid with a mass of 10 kg is heated from 25oC to 200oC. If the change in the specific internal energy is found
to be 67.55 kJ/kg, identify the material. [Manual Solution] [TEST Solution]
Answers: Copper
A block of aluminum with a mass of 10 kg is heated from 25oC to 200oC. Determine (a) the total change in internal
energy and (b) entropy of the block. (c) What-if-Scenario: How would the answer in (b) change if the block was made of
copper instead? [Manual Solution] [TEST Solution]
Answers: (a) 1578.5 kJ/kg (b) 4.17 kJ/K (c) 1.783 kJ/K
A 2 kg block of aluminum at 600oC is dropped into a cooling tank. If the final temperature at equilibrium is 25oC,
determine (a) Change in internal energy, and (b) change in entropy of the block as the system. Use the SL model for
aluminum (c_v = 0.902 kJ/kg.K). [Manual Solution*] [TEST Solution*]
Answers: (a) -1037.3 kJ (b) -1.939 kJ/K
10 A copper block of mass 5 kg, initially at equilibrium with the surroundings at 30oC and 100 kPa is placed in a
pressurized chamber with a pressure of 20 MPa and a temperature of 200oC. Determine (a) the change in the internal
energy (b) enthalpy and (c) entropy of the block after it comes to a new equilibrium. (d) What-if-Scenario: How would
the answer in (a) change if the block was made of silver? [Manual Solution] [TEST Solution]
Answers: (a) 65.62 kJ/kg (b) 67.85 kJ/kg (c) 0.17 kJ/kg.K (d) 39.94 kJ/kg
A 2 kg block of aluminum at 60oC is dropped into a tank containing 5 kg of water at 25oC. If the final temperature after
equilibrium is 27.77oC. Determine (a) DU and (b) DS for the combined system of aluminum and water before and after
the process. [Manual Solution] [TEST Solution]
Answers: (a) -52.35 kJ (b) -0.1643 kJ/K
] A cup of coffee cools down by transferring heat to the surroundings at a rate of 0.1 kW. If the mass of coffee is 0.2 kg
and coffee can be modeled as water, determine the rate of change of temperature of coffee. [Manual Solution][TEST
Solution]
Answers: (a) 1.2 K/s Anim. 3-2-14 (click)
A pump raises the pressure of liquid water from 50 kPa to 5000 kPa in an isentropic manner. Determine (a) the change
in temperature and (b) specific enthalpy between the inlet and exit. [Manual Solution] [TEST Solution]
 
Ct
tt
tt



9827
85022346488366982355
40194120019493348022220
.
...
))(.()(..)(.

53. Answers: (a) 0 (b) 4.965 kJ/kg
Oil (cv=1.8 kJ/kg.K) flows steadily through a long insulated constant-diameter pipe at a volume flow rate of 10 m3/min.
The conditions at the inlet are p = 3000 kPa, T = 20oC, V=20 m/s and z=100 m. The conditions at the exit are p = 2000
kPa, T = 21oC and z=0 m. (a) Use the mass equation to evaluate the velocity at the exit. (b) Use the energy equation
to show that j remains unchanged between the inlet and the exit. (c) Determine the exit temperature. [Manual Solution]
[TEST Solution]
Answers: (a) 20 m/s (b) 21.16oC
Water flows steadily through a device at a flow rate of 20 kg/s. At the inlet the conditions are 200 kPa and 10oC. At the
exit the conditions are 2000 kPa and 50oC. (a) Determine the difference between the entropy transported by the flow at
the exit and at the inlet. (b) What are the possible reasons behind the increase in entropy transport? [Manual Solution]
[TEST Solution]
Answers: (a) 11.06 kW/K (b) heat addition and irreversibilities
19 In an isentropic nozzle, operating at steady state, the specific flow energy 'j' and specific entropy 's' remain constant
along the flow. The following properties are known at the inlet and exit ports of an isentropic nozzle discharging water
at a steady rate of 2 kg/s. Inlet: p=300 kPa, A=4 cm2; Exit: p=100 kPa. Determine (a) the exit velocity and (b) the exit
area. Use the SL model for liquid water. (c) What-if scenario: How would the exit velocity change if the inlet kinetic
energy was neglected? [Manual Solution] [TEST Solution]
Answers: (a) 20.65 m/s (b) 97.2 mm2 (c) 20.03 m/s Anim. 3-2-19 (click)
A pipe carries saturated liquid water at a pressure of 500 kPa. Some water squirts out from the pipe through a small
leak. As the water is expelled, it quickly achieves mechanical equilibrium with the atmosphere at 100 kPa. (a) Estimate
the temperature of water inside and outside the pipe. What if scenario: How would the answers change if the fluid was
(b) R-134a or (c) R-12 instead? [Manual Solution] [TEST Solution]
Answers: (a) 151.8oC, 99.6oC (b) 15.6oC, -26.6oC (c) 15.6oC, -30.1oC
A vertical piston-cylinder assembly contains water. The piston has a mass of 2 kg and a diameter of 10 cm. Determine
the vertical force necessary on the piston to ensure that water inside the cylinder boils at (a) 120oC or (b) 80oC. Assume
atmospheric pressure to be 101 kPa. (c) What-if scenario: How would the answer in part (a) change if the piston mass
was neglected? [Manual Solution] [TEST Solution]
Answers: (a) 0.746 kN (b) -0.441 kN (c) 0.766 kN Anim. 3-3-8 (click)
A vertical piston-cylinder assembly contains a saturated mixture of water at 120oC and a gage pressure of 108.5 kPa.
The piston has a mass of 5 kg and a diameter of 12 cm. Determine (a) the atmospheric pressure outside and (b) the
external force exerted on the piston to maintain a constant pressure. [Manual Solution]
Answers: (a) 90 kPa (b) 1.178 kN downward
A cooking pan with an inner diameter of 20 cm is filled with water and covered with a lid of mass 5 kg. If the atmospheric
pressure is 100 kPa. Determine (a) the boiling temperature of water. (b) What-if-Scenario: How would the answer
change if a 5 kg block is placed on top of the lid? [Manual Solution] [TEST Solution]
Answers: (a) 100.04 oC (b) 100.45 oC. Anim. 3-3-10 (click)
11 A heat engine cycle is executed with ammonia in the saturation dome. The pressure of ammonia is 1.5 MPa during
heat addition and 0.6 MPa during heat rejection. What is the highest possible thermal efficiency? Based on the
temperatures of heat addition and rejection, could you comment on possible application of such a low-efficiency cycle?
[Manual Solution] [TEST Solution]
Answers: 9.44% Anim. 3-3-11 (click)
16 A 10 L rigid tank contains 0.01 kg of steam. Determine the (a) pressure (b) stored energy E and (c) entropy S of
steam if the quality is 50%. Neglect kinetic and potential energy. (d) What-if scenario: How would the answers change
if the quality was 100%? [Manual Solution] [TEST Solution]
Answers: (a) 83.7 kPa (b) 14.48 kJ (c) 0.043 kJ/K (d) 175.4 kPa, 25.25 kJ, 0.072 kJ/K Anim. 3-3-16 (click)
A tank contains 20 kg of water at 85oC. If half of it (by mass) is in the liquid phase and the rest in vapor phase, determine
(a) the volumetric quality, and the stored energy in the (b) liquid and (c) vapor phases. [Manual Solution] [TEST Solution]
Answers:(a) 99.96% (b) 99.96% (c) 3558.4 kJ (d) 24,883.5 kJ
A vessel having a volume of 0.5 m3 contains 2 kg saturated liquid and saturated vapor mixture of H2O at 500 kPa.
Calculate the (a) mass and (b) volume of each phase. [Manual Solution] [TEST Solution]