Question

The operating temperature of a cold storage is -9°C and load for the refrigeration plant is 20 kW for ambient temperature of 24°C. The actual COP of the plant used is one fourth that of ideal plant working between the same temperature. The power required to drive the plant is:  
1. 2.5 kW
2. 5 kW
3. 10 kW
4. 3 kW

Answer 1

Correct Answer - Option 3 : 10 kW

Concept:

We know COP of a refrigerator is given by:

\((COP)_{actual}=\frac{Refrigeration\ Effect}{Work\ Input}\)

For reversible refrigerator, COP can be calculated by:

\((COP)_{ideal} = \frac{T_L}{T_H-T_L}\)

where TH = Absolute higher temperature, TL = Absolute lower temperature

Calculation:

Given:

TH = 24°C = 297 K, T = -9°C = 264 K, Refrigeration Effect = 20 kW, COPactual = \(\frac{1}{4}\) × COPideal

 \(COP_{ideal} = \frac{264}{297-264}\)

\(COP_{ideal} = \frac{264}{33}\)

COPideal = 8

∴ COPactual = \(\frac{1}{4}\) × 8 = 2

Now, \((COP)_{actual}=\frac{Refrigeration\ Effect}{Work\ Input}\)

\(2=\frac{20}{Work\ Input}\)

Work Input = 10 kW

Hence the power required to drive the plant is 10 kW.