ASEN 3113 Thermodynamics and Heat Transfer
Homework #5
Assigned: October 12, 2006
Due: October 19, 2006 (class time)
(Total points noted in each section; must clearly show equations with values and units, drawings,
assumptions, etc.)
1. (20 points, 15 points for equations, 5 points for correct answer)
A cold storage room is being used to store strawberries at 1°C. The evaporator and condenser
temperatures are -2 and 45°C, respectively. The refrigeration load is 15 tons (1 ton of
refrigeration load = 3.517 kW). Assume the refrigerant is R-134a. Determine the following:
(a) The refrigerant flow rate
(b) The compressor power requirement
(c) COP
(d) The heat rejected in the condenser
2. (20 points, 15 points for equations, 5 points for correct answer)
For a refrigeration system using R -134a, the evaporator temperature is -5°C, however the
refrigerant entering the compressor is at 5°C. The condenser temperature is 35°C, but the
refrigerant entering the expansion valve is at 30°C.
(a) What is the amount of superheating and subcooling?
(b) If the refrigeration load is 3 tons, calculate the COP for this system.
3 (20 points, 15 points for equations, 5 points for correct answer)
A turbojet aircraft is flying with a velocity of 220 m/s at an altitude of 5800 m. The pressure
ratio across the compressor is 14, and the temperature at the turbine inlet is 1440 K. Assume
ideal operations for all components and ideal gas constant specific heats at the altitude
temperature. Determine the following:
(a) The pressure at the turbine exit
(b) The velocity of the exhaust gases
(c) The propulsive efficiency
4 (20 points, 15 points for equations, 5 points for correct answers)
Consider a 100 MW steam power plant operating as an ideal rankine cycle. The condenser
pressure is 8kPa. The turbine can operate at two pressures, 18 MPa or 4 MPa. Determine for
each of the turbine pressures:
(a) Mass flow rate of steam
(b) Heat transfer rate of the working fluid passing through the condenser and boiler.
(c) Thermal efficiency
Soln:
For the cycle the net power output is
w cycle  w t  w p  m h1  h2   (h4  h3 ) ,
Thus
m 
w cycle
(h1  h2 )  (h4  h3 )
The working fluid passing throough the boiler experiences heat transfer at a rate
Q in  m (h1  h4 )
and in the condenser
Q out  m (h2  h3 )
The thermal efficiency of the cycle is

w cycle
Q
in
a) P1=18 Mpa
State 1: P1 = 18MPa, saturated vapor h1=2509.1 KJ/kg, s1=5.1044 KJ/kg
s2  s f
 0.591, h2  1594.1kJ
State 2: P2 = 8kPA, s2=s1   
sg  s f
State 3: P3 = 8kPa, saturated liquid  h3=173.88 kJ/kg
State 4: h4 = h3 + v3(P4-P3); h3 = 173.88 kJ/kg, v3 = 1.0084x10-3 m3/kg
 h4 = 192.02 kJ/kg
Therefore m 
w cycle
(h1  h2 )  (h4  h3 )
= 4.014x105kg/h
And Q in  m (h1  h4 ) = 258.4x103kW
And Q out  m (h2  h3 ) = 158.4x103 kW
Therefore  
w cycle
= 0.387
Q
in
b) P1= 4 Mpa
State 1: P1 = 4MPa, saturated vapor h1=2801.4 KJ/kg, s1=6.0701 KJ/kg
s2  s f
 0.7173, h2  1897.6kJ
State 2: P2 = 8kPA, s2=s1   
sg  s f
State 3: P3 = 8kPa, saturated liquid  h3=173.88 kJ/kg
State 4: h4 = h3 + v3(P4-P3); h3 = 173.88 kJ/kg, v3 = 1.0084x10-3 m3/kg
 h4 = 1177.91 kJ/kg
Therefore m 
w cycle
(h1  h2 )  (h4  h3 )
= 4.001x105kg/h
And Q in  m (h1  h4 ) = 291.6x103kW
And Q out  m (h2  h3 ) = 191.6x103 kW
Therefore  
w cycle
= 0.343
Q
in
5 (20 points, 15 points for equations, 5 points for correct answers)
(a) A steam power plant is operating as a regenerative vapor power cycle with one closed
feedwater heater that tap off between the first and second turbine stages. The turbine inlet
conditions are pressure 12 Mpa, temperature 510 C. Condenser pressure is 6 kPa. Boiler inlet
temperature is 170 C. Work of the cycle is 320 MW. Determine:
(a) Thermal efficiency
(b) Mass flow rate into the turbine first stage
Assumptions:
(1) Each component is analyzed as a control volume at steady state.
(2) All processes are internally reversible except fro the expansion through the trap
(throttling process) and in the closed feedwater heater.
(3) Turbines, pump, and feedwater heater operate adiabatically.
(4) Kinetic and potential energy functions are negligible.
(5) Condensate exists in the condenser and closed heater as saturated liquid at the respective
pressures.
1 bar = 100kPa
Soln: Fix each of the principal points.
State 1: P1 = 12 MPa, T1 = 520 C  h1 = 3401.8 kJ/kg, s1 = 6.5555 kJ/kg K
State 2: P2 = 1 MPa, s1 = s2  χ2 = 0.9931, h2 = 2764.2 kJ/kg
State 3: P3 = 6 kPa, s3 = s1  χ3 = 0.7727, h3 = 2018.3 kJ/kg
State 4: P3 = 6 kPa, saturated liquid  h4 = 151.53 kJ/kg
State 5: h5 = h4 + v4(P5-P4), v4 = 1.0064x103 m3/kg  163.6kJ/kg
State 6: P6 = 12 MPa, T6 = 170 C  h6 = 725.86 kJ/kg
State 7: P7 = 1 MPa, sat liquid  h7 = 762.81 kJ/kg
State 8: Throttling Process  h8 = h7 = 762.81 kJ/kg
a) Applying mass and energy rate balances to the control volume surrounding the closed
feedwater heater, the fraction of flow y extracted at location 2 is;
h6  h5
 0.2809
h2  h7
For the control volume surrounding the turbine stages
y
w t
 (h1  h2 )  (1  y)( h2  h3 )  1174.0kJ / kg
m 1
And for the pump
w p
 (h5  h4 )  12.07kJ / kg
m 1
For the working fluid passing through the steam generator
Q in
 (h1  h6 )  2675.9kJ / kg
m 1
Thus the thermal efficiency is
 w t   w p
   
m
m
 1  1
Q in
m 1


  0.434
(b) The mass flow rate into the first turbine stage is found from:
m 1 
w cycle
 w t   w p
   
 m 1   m 1



 9.91x10 5 kg / h