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MHT CET · Physics · Thermodynamics

An ideal refrigerator has freezer at a temperature of \(-13^{\circ} \mathrm{C}\). The coefficient of performance of the engine is 5 . The temperature of the air (to which heat is rejected) is

  1. A \(320^{\circ} \mathrm{C}\)
  2. B \(39^{\circ} \mathrm{C}\)
  3. C \(325 \mathrm{K}\)
  4. D \(325^{\circ} \mathrm{C}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(39^{\circ} \mathrm{C}\)

Step-by-step Solution

Detailed explanation

\(\begin{array}{ll} & \text { Coefficient of performance, } \beta=\frac{\mathrm{T}_2}{\mathrm{~T}_1-\mathrm{T}_2} \\ & \text { Given that, } \beta=5 \text { and } \mathrm{T}_2=-13^{\circ} \mathrm{C}=260 \mathrm{~K} \\ \therefore & \frac{260}{\mathrm{~T}_1-260}=5 \\ \therefore & 5 \mathrm{~T}_1-1300=260 \\ \therefore \quad & \mathrm{T}_1=\frac{1560}{5}=312 \mathrm{~K} \\ \therefore \quad & \mathrm{T}_1=39^{\circ} \mathrm{C}\end{array}\)