An ideal refrigerator has freezer at a temperature of $-13^{\circ} \mathrm{C}$. The coefficient of…

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. $320^{\circ} \mathrm{C}$
  2. $39^{\circ} \mathrm{C}$
  3. $325 \mathrm{K}$
  4. $325^{\circ} \mathrm{C}$

Solution

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

Asked in: MHT CET 2023 (14 May Shift 2)

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