8-81
8-123E Argon enters an adiabatic compressor with an isentropic efficiency of 80% at a specified state, and leaves at a
specified pressure. The exit temperature of argon and the work input to the compressor are to be determined.
Assumptions 1 This is a steady-flow process since there is no change with time. 2 Potential energy changes are negligible. 3
The device is adiabatic and thus heat transfer is negligible. 4 Argon is an ideal gas with constant specific heats.
Properties The specific heat ratio of argon is k = 1.667. The constant pressure
specific heat of argon is cp = 0.1253 Btu/lbm.R (Table A-2E).
Analysis (a) The isentropic exit temperature T2s is determined from
psia 200
70.667/1.66
/1
2
kk
s
P
/sft 25,037
2
222
The effect of kinetic energy on isentropic efficiency is very small. Therefore, we can take the kinetic energy changes for the
actual and isentropic cases to be same in efficiency calculations. From the isentropic efficiency relation, including the effect
outin
energies etc. potential,
kinetic, internal,in change of Rate
(steady ) 0
sy stem
mass and work,heat,by
nsferenergy tranet of Rate
outin 0
EE
EEE
a12a12ina,
1
2
12ina,
2
22
2
11ina,
Δke)(Δke
2
0)pe (since /2)+()2/(
TTchhwhhmW
QVhmVhmW
ap
VV
Substituting, the work input to the compressor is determined to be
Ar
2
1
8-83
8-125E Problem 8-124E is reconsidered. The effect of varying the nozzle isentropic efficiency from 0.8 to 1.0 on the
exit temperature and pressure of the air is to be investigated, and the results are to be plotted.
Analysis The problem is solved using EES, and the results are tabulated and plotted below.
“Knowns:”
WorkFluid$ = ‘Air’
P_2_answer = P[2]
0.8 0.84 0.88 0.92 0.96 1
41.2
8-84
8-126 Air is expanded in an adiabatic nozzle with an isentropic efficiency of 0.96. The air velocity at the exit is to be
determined.
K 331.0
kPa 300
kPa 100
K) 273(180
4.1/4.0
/)1(
1
2
12
kk
sP
P
TT
outin
energies etc. potential,
kinetic, internal,in change of Rate
(steady) 0
system
mass and work,heat,by
nsferenergy tranet of Rate
outin 0
EE
EEE
ke
2
)(
2
22
22
2
1
2
2
21
2
1
2
2
21
2
2
2
2
1
1
2
2
2
2
1
1
VV
TTc
VV
hh
V
h
V
h
V
hm
V
hm
p
300 kPa
8-86
8-128 Hot combustion gases are accelerated in a 92% efficient adiabatic nozzle from low velocity to a specified velocity.
The exit velocity and the exit temperature are to be determined.
8-129E Refrigerant-134a is expanded adiabatically from a specified state to another. The entropy generation is to be
determined.
Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential energy changes are negligible.
Analysis The rate of entropy generation within the expansion device during this process can be determined by applying the
8-88
8-130 Oxygen is cooled as it flows in an insulated pipe. The rate of entropy generation in the pipe is to be determined.
Assumptions 1 Steady operating conditions exist. 2 The pipe is well-insulated so that heat loss to the surroundings is
negligible. 3 Changes in the kinetic and potential energies are negligible. 4 Oxygen is an ideal gas with constant specific
heats.
Properties The properties of oxygen at room temperature are R = 0.2598 kJ/kgK, cp = 0.918 kJ/kgK (Table A-2a).
8-89
8-131 Nitrogen is compressed by an adiabatic compressor. The entropy generation for this process is to be determined.
Assumptions 1 Steady operating conditions exist. 2 The compressor is well-insulated so that heat loss to the surroundings is
negligible. 3 Changes in the kinetic and potential energies are negligible. 4 Nitrogen is an ideal gas with constant specific
heats.
Properties The specific heat of nitrogen at the average temperature of (25+290)/2=158C = 431 K is cp = 1.047 kJ/kgK
8-94
8-136E Steam is condensed by cooling water in a condenser. The rate of heat transfer and the rate of entropy generation
within the heat exchanger are to be determined.
1007.8 Btu/lbm and sfg = 1.6529 Btu/lbm.R (Table A-4E).
Analysis We take the tube-side of the heat exchanger where cold water is
150F
73F
8-96
8-138 Ethylene glycol is cooled by water in a heat exchanger. The rate of heat transfer and the rate of entropy generation
within the heat exchanger are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the
surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes
in the kinetic and potential energies of fluid streams are negligible. 4 Fluid properties are constant.
8-97
8-139 Oil is to be cooled by water in a thin-walled heat exchanger. The rate of heat transfer and the rate of entropy
generation within the heat exchanger are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The heat exchanger is well-insulated so that heat loss to the
surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold fluid. 3 Changes
in the kinetic and potential energies of fluid streams are negligible. 4 Fluid properties are constant.
)(
0)peke (since
21out
2out1
outin
TTcmQ
hmQhm
p
Then the rate of heat transfer from the oil becomes
=C)40CC)(150kJ/kg. kg/s)(2.2 2()]([ oiloutinout kW 484 TTcmQ p
Noting that the heat lost by the oil is gained by the water, the outlet temperature of the water is determined from
C2.99
C)kJ/kg. (4.18 kg/s) (1.5
kW 484
C20)]([ in
inoutwaterinoutin
p
pcm
Q
TTTTcmQ
(b) The rate of entropy generation within the heat exchanger is determined by applying the rate form of the entropy balance
on the entire heat exchanger:
)()(
0
34water12oilgen
gen4water2oil3water1oil
gen43223311
entropy of
change of Rate
(steady) 0
system
generation
entropy of Rate
gen
mass andheat by
ansferentropy trnet of Rate
outin
ssmssmS
Ssmsmsmsm
SSSS
Noting that both fluid streams are liquids (incompressible substances), the rate of entropy generation is determined to be
273+99.2
273+40
lnln
3
4
water
1
2
oilgen T
T
cm
T
T
cmS pp
22C
1.5 kg/s
40C
8-99
8-141 An egg is dropped into boiling water. The amount of heat transfer to the egg by the time it is cooked and the amount
of entropy generation associated with this heat transfer process are to be determined.
Assumptions 1 The egg is spherical in shape with a radius of r0 = 2.75 cm. 2 The thermal properties of the egg are constant.
3 Energy absorption or release associated with any chemical and/or phase changes within the egg is negligible. 4 There are
kJ 18.3
C)870)(CkJ/kg. 32.3)(kg 0889.0()(
kg 0889.0
6
m) 055.0(
)kg/m 1020(
6
12in
3
3
3
TTmcQ
D
m
p
V
Egg
8C
