First slide

Heat Engine; Carnot Engine and refrigerator

Question

A freezer has coefficient of performance equal to 5. When $3.6 \times 10^{6}$ J work is done on the freezer, what mass of water at 0⁰C is converted into ice cubes at 0⁰C.

Moderate

A

$\approx$ 5kg
B

$\approx$ 3.6kg
C

$\approx$ 54kg
D

$\approx$ 107kg

Solution

We know, Coefficient of Performance, $COP = \frac{Q}{W}$
And $Q = m L$ and latent heat of fusion of water, $L = 334 \times 10^{3} J k g^{- 1}$
Hence, $m = \frac{C O P \times W}{L} = \frac{5 \times 3.6 \times 10^{6}}{334 \times 10^{3}} = 53.8 k g$

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