13468-11-69P AID: 1825 | 05/12/2014

Show the ideal-gas refrigeration cycle, with air as the working fluid, on diagram as in Figure (1).

For the given ideal-gas refrigeration cycle, with air as the working fluid, temperature, specific enthalpy, pressure, and relative pressure at state are , , , and respectively.

(a)

For the given ideal-gas refrigeration cycle with air as the working fluid, both the turbine and the compressor are isentropic. Also, the turbine inlet temperature is the temperature of the surroundings, and the compressor inlet temperature is the temperature of the refrigerated space.

Use ideal-gas properties of air table, to find and of air, at .

Use ideal-gas properties of air table, to find and of air at 300 K .

Express the pressure relation ratio for the process 1-2, to find the relative pressure at state 2.

Substitute 3 for , and 0.7329 for

Use ideal-gas properties of air table, to find of air at 2.1987 . Use interpolation method to find .

Use ideal-gas properties of air table, to find of air at 2.1987 . Use interpolation method to find .

Hence, the maximum temperature in the ideal-gas refrigeration cycle is .

Express the pressure relation ratio for the process 3-4, to find the relative pressure at state 4.

Substitute for , and 1.386 for

Use ideal-gas properties of air table, to find of air at 0.462 . Use interpolation method to find .

Use ideal-gas properties of air table, to find of air at 0.462 . Use interpolation method to find .

Hence, the minimum temperature in the ideal-gas refrigeration cycle is .

(b)

Find the COP of the given ideal gas refrigeration cycle .

(1)

Here, the amount of heat per unit mass removed from the refrigerated space is , the specific work input to the compressor is , and the specific work output from the turbine is ,and the net specific work input for the ideal-gas refrigeration cycle is .

Calculate the amount of heat per unit mass, removed from the refrigerated space .

Substitute for , and for .

Calculate the specific work input to the compressor .

Substitute for , and for .

Calculate the specific work output from the turbine .

Substitute for , and for .

Substitute for , for , and for in Equation (1) to find .

Hence, the COP for the given ideal-gas refrigeration cycle is .

(c)

Find the rate of refrigeration for the given ideal-gas refrigeration cycle .

Here, the mass flow rate of air is .

Substitute for , and for .

Hence, the rate of refrigeration for the given ideal-gas refrigeration cycle is .