A Carnot's engine works as a refrigerator between \(250\, K\) and \(300\, K\). It receives \(500\, cal\) heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is ..... \(J\)

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Answer & Solution

Correct Answer

(A) \(420\)

Detailed explanation

Given: Temperature of cold body, \(T_2= 250\,K\) temperature of hot body; \(T_1 = 300\, K\) Heat received, \(Q_2= 500\, cal\) work done, \(W =\) ?

Effociency\( = 1 - \frac{{{T_2}}}{{{T_1}}} = \frac{W}{{{Q_2} + W}}\)

\( \Rightarrow 1 - \frac{{250}}{{300}} = \frac{W}{{{Q_2} + W}}\)

\(W = \frac{{{Q_2}}}{5} = \frac{{500 \times 4.2}}{5}\,\,J = 420\,J\)

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