# A cold storage plant of 20 tonne of refrigerator capacity operates between 200 K and 300 K. The power required to run the plant if the plant has half

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A cold storage plant of 20 tonne of refrigerator capacity operates between 200 K and 300 K. The power required to run the plant if the plant has half COP of a Carnot cycle (Tonne of refrigerator = 3.5 kW) is
1. 50 kW
2. 60 kW
3. 70 kW
4. 80 kW

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Correct Answer - Option 3 : 70 kW

Concept:

The COP of refrigerator is given as,

Ideal $COP = \frac{{{T_L}}}{{{T_H} - {T_L}}}$ and Actual $COP = \frac{Q}{W_{input}}$

Calculation:

Given:

Q̇ = 20 × 3.5 = 70 kW, TL = 200 K, TH = 300 K

Ideal $COP = \frac{{{200}}}{{{300} - {200}}}$ = 2

Actual COP = $\frac{1}{2}$ × Ideal COP = $\frac{1}{2}$ × 2 = 1

Actual COP = 1

Also, Actual COP = $\frac{{\dot Q}}{{\dot W}} = \frac{{70}}{{\dot W}}$

$\dot {W}$ = 70 kW.