EGR 334 Thermodynamics: Homework 19
Problem 4: 94
For review complete the following: Answer True or false and explain.
----------------------------------------------------------------------------------------------------------------------------- ----------a i) For a one-inlet, one-exit CV at SS, the mass flow rates at the inlet and exit are equal, but the inlet and exit
volumetric flow rates may not be equal.
True
----------------------------------------------------------------------------------------------------------------------------- ----------a ii) Flow work is the work done on a flowing stream by a paddlewheel or piston.
False . Flow work is the work needed get the flowing mass to its compressed state
----------------------------------------------------------------------------------------------------------------------------- ----------a iii) Transient operation denotes a change in state with time.
True
----------------------------------------------------------------------------------------------------------------------------- ----------a iv) In this book the flow at CV inlets and exits is normally taken as one-dimensional
True
----------------------------------------------------------------------------------------------------------------------------- ----------a v) Where mass crosses the boundary of a CV, the accompanying energy transfer is accounted for by the internal
energy of the mass only.
False, energy transfer due to mass also includes potential and kinetic energies
----------------------------------------------------------------------------------------------------------------------------- ----------b i) A diffuser is a flow passage of varying cross sectional area in which the velocity of a gas or liquid increases in
the direction of flow.
False, the velocity decreases in the direction of flow…a nozzle increases flow speed.
---------------------------------------------------------------------------------------------------------------------------------------b ii) The human body is an example of an integrated system.
True
---------------------------------------------------------------------------------------------------------------------------------------b iii) When a substance undergoes a throttling process through a valve, the specific enthalpies of the substance at
the valve inlet and value exit are equal.
True
---------------------------------------------------------------------------------------------------------------------------------------b iv) The hot and cold streams of cross flow heat exchangers flow in the same direction.
False. they flow perpendicular to each other
----------------------------------------------------------------------------------------------------------------------------- ----------b v) The thermodynamic performance of a device such as a turbine through which mass flows is best analyzed by
studying the flowing mass alone.
False, energy flow is more important, since the mass flow is pretty constant in the turbine.
----------------------------------------------------------------------------------------------------------------------------- ----------c i) for every control volume at steady state, the total of the entering rates of mass flow equals the total of the exiting
rates of mass flow.
True
----------------------------------------------------------------------------------------------------------- ----------------------------c ii) An open feed-water heater is a special type of a counter-flow heat exchanger.
False, I wouldn't really call it a counter flow exchanger at all. Maybe it could be a special case of a cross
flow exchanger.
--------------------------------------------------------------------------------------------------------------------------------------- c iii) A key step in thermodynamic analysis is the careful listing of modeling assumptions.
True
-----------------------------------------------------------------------------------------------------------------------------------------c iv) An automobile's radiator is an example of a cross flow heat exchanger.
True
-----------------------------------------------------------------------------------------------------------------------------------------c v) At steady state, identical electric fans discharging air at the same temperature in NYC and Denver will deliver
the same volumetric flow rate of air.
True, but the fans will likely have different mass flow rates since air densities will be different.
EGR 334 thermodynamics: homework 19
Problem 4: 100
Carbon dioxide modeled as ideal gas flows through the compressor and heat exchanger shown. The power input to
the compressor is 100 kW. A separate liquid cooling water stream flows through the heat exchanger. All given
data is at steady state. Stray heat transfer with the surroundings can be neglected. Determine
a) mass flow rate of the CO2 in kg/s
b) the mass flow rate of the cooling water in kg/s
-----------------------------------------------------------------CO2 as ideal gas
Cooling water
State 1: p1 = 100 kPa
T 4 = 20 C
T1 = 280 K
State 2: p2 = 1 MPa
T 5 = 30 C
T2 = 500 K
State 3: T3 = 350 K
Wcompressor = 100 kW.
From Table A-20, use cp(T=400K) ≈ 0.939 kJ/kg-K
Compressor Model:
0  W  mCO 2 (h1  h2 )
0  (Wcompressor )  mCO2 c p (T1  T2 )
mCO 2 
Wcompressor
cv (T2  T1 )

100kW
kJ / s
 0.484kg / s
(0.939kJ / kg  K )(500  280) K kW
Heat Exchanger Model:
0  mCO 2 (h2  h3 )  mH 20 (h4  h5 )
0  mCO 2cv (T2  T3 )  mH 20 (h4  h5 )
m c (T  T )
mH 20  CO 2 v 3 2
(h4  h5 )
where h4=hf(T=20C) = 83.96 kJ/kg
mH 20 
and h5=hf(T=30C)= 125.79 kJ/kg
(0.484kg / s)(0.939kJ / kg  K ))(350  500) K
 1.63kg / s
(83.96  125.79)kJ / kg
EGR 334 Thermodynamics: Homework 19
Problem 4: 106
A simple gas turbine power cycle operating at steady state with air as the working substance is shown. The cycle
components include an air compressor mounted on the same shaft as the turbine. The air is heated in the high
pressure heat exchanger before entering the turbine. The air exiting the turbine is cooled in the lower pressure heat
exchanger before returning to the compressor. KE and PE effects are small. The compressor and turbine are
adiabatic. Using the ideal gas model for air, determine
a) power required for the compressor in hp
b) the power output of the turbine in hp
c) the thermal efficiency of the cycle.
--------------------------------------------------------------------Ideal gas model with Air.
State 1: p1 = 1 atm
T1 = 520 R
(AV)1 = 30000 ft3/min
State 2: T2 = 650 R
State 3: p3= p2
T3 = 2000 R
State 4: p4 = p1 = 1 atm
T4 = 980 R
R for air = 0.06855 Btu/lbm-R
cp(520 R) = 0.248 Btu/lbm-R
cp(650 R) =0.252 Btu/lbm-R
cp(2000 R)=0.286 Btu/lbm-R
cp(980R) =0.259 Btu/lbm-R
from state 1 and ideal gas law:
pV  mRT
2
p1 ( AV)1
pV
(1atm)(30000 ft 3 / min) 14.7lb f / in
Btu
144in 2
m


 2290 lbm / min
RT
RT1
(0.06855 Btu / lbm  R)(520 R)
atm
778lb f  ft 1 ft 2
Energy balance:
0  Q  W  mi (hi 
Process 1-2:
Vi 2
V2
 gzi )  me (he  e  gze )
2
2
adiabatic, no change of KE or PE.
Use cp_ave = 0.250 Btu/lbm-R
0  (Wcompressor )  m(h1  h2 )
Wcompressor  m(h2  h1 )  mc p (T2  T1 )  (2290lbm / min)(0.250Btu / lbm - R)(650  520)R
 74425Btu / min  1754.6HP
Process 2-3: W= 0 and no change of KE or PE Use cp_ave = 0.269 Btu/lbm-R
0  Qin  m(h2  h3 )
Qin  m(h3  h2 )  mcp (T3  T2 )  (2290lbm / min)(0.269Btu / lbm  R)(2000  650)R
 831613.5Btu / min
Process 3-4: adiabatic, no change of KE or PE.
cp_ave = 0.273 Btu/lbm-R
0  Wcompressor  Wnet  m(h3  h4 )
Wnet  m(h3  h4 )  Wcompressor  (2290lbm / min)(0.273Btu / lbm  R)(2000  980) R  74425Btu / min
 563248 Btu / min  13279 HP
Process 4-1: no change of KE or PE
c p_ave = 0.254 Btu/lbm-R
0  Qout  m(h4  h1 )
Qout  m(h4  h1 )  mc p (T4  T1 )  (2290lbm / min)(0.254Btu / lbm  R)(980  520)R
 267653 Btu / min
Therefore the power output of the turbine is
Wnet  563248 Btu / min
and the thermal efficiency may be found as

Wnet
563248 Btu / min

 0.677  67.7%
Qin 831613.5Btu / min