MHT CET · Physics · Thermodynamics

If $α$ is the coeﬃcient of performance of a refrigerator and ‘ $Q_{1}$ ’ is heat released to the hot reservoir, then the heat extracted from the cold reservoir ‘ $Q_{2}$ ’ is

A $\frac{α Q_{1}}{α - 1}$
B $\frac{α - 1}{α} Q_{1}$
C $\frac{α Q_{1}}{1 + α}$
D $\frac{1 + α}{α} Q_{1}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{α Q_{1}}{1 + α}$

Step-by-step Solution

Detailed explanation

∵ α = \frac{Q_{2}}{Q_{1} - Q_{2}}

\Rightarrow \propto Q_{1} - \propto Q_{2} = Q_{2}

\Rightarrow Q_{2} = \frac{\propto Q_{1}}{1 + \propto}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If α is the coeﬃcient of performance of a refrigerator and ‘ Q1 ’ is heat released to the hot reservoir, then the heat extracted from the cold reservoir ‘ Q2 ’ is

Step-by-step Solution

If $α$ is the coeﬃcient of performance of a refrigerator and ‘ $Q_{1}$ ’ is heat released to the hot reservoir, then the heat extracted from the cold reservoir ‘ $Q_{2}$ ’ is