Question

A refrigerator removes heat from a refrigerated space at -6°C and rejects it to an environment at 30°C. If the temperature in the cooled area is reduced to - 18°C, determine the minimum percentage increase in the work required for the same amount of energy from which the Carnot refrigerator is removed.

a. 53

b. 33

c. 93

d. 13

e. 73

Answer 1

Calculations for finding out minimum increase in work required for Carnot refrigerator is done below.

Notations used:

• TH= Temperature of the environment.
• TL= Temperature of the refrigerated space.
• QH= Energy removed from the Carnot refrigerator.
• QL= Energy removed from refrigerated space
• W= Work required for the refrigerator.
• COP= Coefficient of performance of refrigerator.
• Suffix-1 is used for the refrigerator operating between -6°C and 30°C.
• Suffix-2 is used for the refrigerator operating between -18°C and 30°C.

Note:

• We know that, COP of refrigerator= TL/(TH-TL)
• We also know that, COP of refrigerator= QL/W
• By first law, QL+ W= QH
• So, QL= QH - W
• So, COP of refrigerator= (QH - W)/W