13468-11-58P AID: 1825 | 05/12/2014

Show the layout of the two-stage cascade refrigeration cycle, with refrigerant-134a as the working fluid as in Figure (1).

For the given ideal vapor-compression refrigeration cycle, with refrigerant-134a as the working fluid, temperature, specific enthalpy, pressure, and specific entropy at state are , , , and respectively. Also, the saturated liquid state is denoted by the subscript f, the saturated vapor is denoted by the subscript g, and the properties at latent stage are denoted by the subscript fg.

(a)

Use saturated refrigerant-134a pressure table, to find and of refrigerant-134a, at .

For the isentropic process 1-2, entropy remains constant. Hence, and are equal.

Use superheated refrigerant-134a table, to find refrigerant-134a, at , and at . Use interpolation method to find .

Express the isentropic efficiency of the compressor in the lower cycle.

Rearrange and substitute for , for , and 0.8 for to find.

Use saturated refrigerant-134a pressure table, to find of refrigerant-134a, at 500 kPa.

For the isenthalpic process 3-4, specific enthalpy remains constant. Hence, and are equal.

Use saturated refrigerant-134a pressure table, to find and of refrigerant-134a, at .

For the isentropic process 5-6, entropy remains constant. Hence, and are equal. Use superheated refrigerant-134a table, to find of refrigerant-134a, at , and at . Use interpolation method to find .

Express the isentropic efficiency of the compressor in the upper cycle.

Rearrange and substitute for , for , and 0.8 for to find.

Use saturated refrigerant-134a pressure table, to find of refrigerant-134a, at 1,400 kPa .

For the isenthalpic process 7-8, specific enthalpy remains constant. Hence, and are equal.

Express the energy balance for the heat exchanger as

Here, the mass flow rate of refrigerant through the upper cycle is , and the mass flow rate for refrigerant through the lower cycle is .

Rearrange and substitute for , for , for , for , and for to find .

Hence, the mass flow rate of refrigerant through the upper cycle is .

(b)

Find the rate of heat removal from the refrigerated space .

Substitute for , for , for .

Hence, the rate of heat removal from the refrigerated space is .

(c)

Find the power input to both the compressors.

Substitute for , for , for , for , for , and for .

Calculate the COP for two-stage cascade refrigeration cycle.

Substitute 18.46 kW for , and 8.511 kW for .

Hence, the COP for the given two-stage cascade refrigeration cycle is .