A Carnot refrigerator absorbs heat from water at 0⁰C and gives it to a room at 27⁰C, when it converts 2 kg of water at 0⁰C into ice at 0⁰C, the work done is (Latent heat of fusions of ice = (333 × 10³Jkg^–1)

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95.52 × 10³J

65.87 × 10³J

25 × 10³J

82 × 10³J

answer is C.

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Detailed Solution

We know that Coefficient of performance
$\begin{array}{l} \frac{Q_{2}}{w} = \frac{T_{2}}{T_{1} - T_{2}} \Rightarrow \frac{{mL}_{ice}}{W} = \frac{T_{2}}{T_{1} - T_{2}} \\ ∴ \frac{2 \times 333 \times 10^{3}}{W} = \frac{273}{27} \\ \Rightarrow W = \frac{27 \times 2 \times 333 \times 10^{3}}{273} \\ = 65 .87 \times 10^{3} J \end{array}$