A gas refrigeration system using air as the working fluid has a pressure ratio of 5. Air enters the compressor at 0°C. The high-pressure air is cooled to 35°C by rejecting heat to the surroundings. The refrigerant leaves the turbine at −80°C and then it absorbs heat from the refrigerated space before entering the regenerator. The mass flow rate of air is 0.4 kg/s. Assuming isentropic efficiencies of 80 percent for the compressor and 85 percent for the turbine and using constant specific heats at room temperature, determine (a) the effectiveness of the regenerator, (b) the rate of heat removal from the refrigerated space, and (c) the COP of the cycle. Also, determine (d) the refrigeration load and the COP if this system operated on the simple gas refrigeration cycle. Use the same compressor inlet temperature as given, the same turbine inlet temperature as calculated, and the same compressor and turbine efficiencies.
FIGURE P11–79
(a)
The effectiveness of the regenerator.
Answer to Problem 79P
The effectiveness of the regenerator is
Explanation of Solution
Show the T-s diagram as in Figure (1).
Express the temperature at state 2s.
Here, temperature at state 1 is
Express the temperature at state 2 from the isentropic relations.
Here, isentropic efficiency is
Express temperature at state 5s.
Here, temperature at state 4 is
Express temperature at state 4.
Here, thermal efficiency is
Express the temperature at state 6 using an energy balance.
Here, mass flow rate is
Express the effectiveness of the regenerator.
Here, enthalpy at state 3, 4 and 6 is
Conclusion:
Perform unit conversion of temperature at state 1, 3, and 5 from
Refer Table A-2, “ideal gas specific heats of various common gas”, and write the properties of air.
Substitute
Substitute
Substitute
Substitute
Solve Equations (VII) and (VIII) simultaneously by online calculator to get,
Substitute
Substitute
Hence, the effectiveness of the regenerator is
(b)
The rate of heat removal from the refrigerated space.
Answer to Problem 79P
The rate of heat removal from the refrigerated space is
Explanation of Solution
Express the rate of heat removal from the refrigerated space.
Conclusion:
Substitute
Hence, the rate of heat removal from the refrigerated space is
(c)
The COP of the gas refrigeration cycle.
Answer to Problem 79P
The COP of the gas refrigeration cycle is
Explanation of Solution
Express the net work input of the compressor.
Express the net work output of the turbine.
Express the coefficient of performance of the gas refrigeration cycle.
Conclusion:
Substitute
Substitute
Substitute
Hence, the COP of the gas refrigeration cycle is
(d)
The refrigeration load and the COP of the system.
Answer to Problem 79P
The refrigeration load is
Explanation of Solution
Show the T-s diagram as in Figure (2).
Express temperature at state 4s.
Here, temperature at state 3 is
Express temperature at state 4.
Express the refrigeration load.
Express the net work input.
Express the coefficient of performance of the system.
Conclusion:
Substitute
Substitute
Substitute
Hence, the refrigeration load is
Substitute
Substitute
Hence, the coefficient of performance of the system is
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Chapter 11 Solutions
THERMODYNAMICS
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