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The cycle operates steadily and uses refrigerant R134a. Determine the rate of cooling of the refrigerated space per kg of R134a (kJ/kg). Indicate the correct answer from the list provided. If none of the choices are within 5% of the correct answer, or if the question is unanswerable, indicate that choice instead.

A. 107 kJ/kg
B. 0.652 kJ/kg
C. 38.8 kJ/kg
D. 0.561 kJ/kg
E. 176 kJ/kg
F. 138 kJ/kg
G. None of these are within 5% of the correct solution
H. 17.2 kJ/kg
I. The question is unanswerable: it is missing information

A simple ideal refrigeration cycle operates between 140 kPa and 900 kPa. The cycle operates steadily and uses refrigerant R134a. Determine the rate of compressor work per kg of R134a (kJ/kg). Indicate the correct answer from the list provided. If none of the choices are within 5% of the correct answer, or if the question is unanswerable, indicate that choice instead.

A. 30.1 kJ/kg
B. 17.2 kJ/kg
C. 38.8 kJ/kg
D. 107 kJ/kg
E. 138 kJ/kg
F. None of these are within 5% of the correct solution
G. 0.652 kJ/kg
H. The question is unanswerable: it is missing information
I. 0.561 kJ/kg
J. 176 kJ/kg

Answer :

The given ideal refrigeration cycle uses refrigerant R134a which operates steadily between 140 kPa and 900 kPa.

We need to determine the rate of cooling of the refrigerated space per kg R134a (kJ/kg).

Let,

h1 = Enthalpy of refrigerant R134a at the beginning of the

processh4 = Enthalpy of refrigerant R134a at the end of the

processh2 = Enthalpy of refrigerant R134a after

compressionh3 = Enthalpy of refrigerant R134a after expansion

The coefficient of performance of a refrigerator (COP) is given by:

COP = (Refrigeration effect) / (Work input)

For a refrigerator,

COP = QL / W = h1 - h4 / h2 - h1

The refrigeration effect per unit mass of the refrigerant is given by:

QL = h1 - h4

The work done per unit mass of the refrigerant is given by:

W = h2 - h3

From the first law of thermodynamics for a cycle,

Work input = QL + W

Here, W is negative as work is done on the system.

The rate of compressor work per kg R134a is 0.652 kJ/kg.

the correct answer is option (g).

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