13468-11-56P AID: 1825 | 05/12/2014

Show the two-stage cascade refrigeration system, with each stage operating on the ideal vapor-compression refrigeration cycle, with refrigerant-134a as the working fluid, on

diagram as in Figure (1).

For the two-stage cascade refrigeration system, with each stage operating on the ideal vapor-compression refrigeration cycle, with refrigerant-134a as the working fluid, the

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

0.14 MPa .

For the isentropic process 1-2, 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 .

Use “saturated refrigerant-134a pressure table”, to find the of refrigerant at 0.4 MPa

.

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 at 0.4

MPa .

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 .

Use “saturated refrigerant-134a pressure table”, to find of refrigerant at 0.8 MPa .

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

Express the energy balance equation for the heat exchanger.

Here, energy entering the system is , energy leaving the system is ,the mass flow

rate of the working fluid flowing out of the system is , specific enthalpy of the

working fluid flowing out of the system is , specific enthalpy of the working fluid

flowing into the system is , the mass flow rate of the working fluid flowing into the

system is , the mass flow rate of refrigerant through the upper cycle is , and the

mass flow rate of 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 lower cycle is .

(b)

Find the rate of heat removed by the Cascade cycle .

Substitute for , for , and for .

Hence, the rate of heat removed by the Cascade cycle is .

Find the work input for the Cascade cycle .

Here, the work input for the first compressor is , and the work input for the

second compressor is .

Substitute for , for , for , for

, for , and for .

Hence, the work input for the Cascade cycle is .

(c)

Find the COP for the given Cascade refrigeration system .

Substitute for , and 34.18 kW for .

Hence, the COP for the given Cascade refrigeration system is .