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  4. 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 :

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Q. 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 :

JEE MainJEE Main 2018Thermodynamics

Solution:

Given: $T_{1}=250\, K ;\, T_{2}=300\, K ;\, Q_{2}=500\, cal$
Efficiency $\eta=\frac{T_{2}-T_{1}}{T_{1}}=\frac{300-250}{250}=\frac{50}{250}=\frac{1}{5}$
Also, efficiency $=\frac{W}{Q_{2}}$
Work done $W =Q_{2} \times \eta=\frac{500\, cal }{5}$
$W =\frac{500 \times 4.184\, J }{5}=420\, J$