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Heat and Thermodynamics question

2023 · Q129
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Heat and Thermodynamics question

2023 · Q129

NEETPhysicsHeat and ThermodynamicsMCQ+4 / −1

A Carnot engine has an efficiency of 50%50 \%50% when its source is at a temperature 327∘C327^{\circ} \mathrm{C}327∘C. The temperature of the sink is :-

  1. A
    15∘C15^{\circ} \mathrm{C}15∘C
  2. B
    100∘C100^{\circ} \mathrm{C}100∘C
  3. C
    200∘C200^{\circ} \mathrm{C}200∘C
  4. D
    27∘C27^{\circ} \mathrm{C}27∘C
View written solutionFree

Correct answer: D

Efficiency of carnot engine

$$ \begin{aligned} & \% \eta=\left(1-\frac{T_{\text {sink }}}{\mathrm{T}_{\text {source }}}\right) \times 100 \\ & T_{\text {source }}=327^{\circ} \mathrm{C}=600 \mathrm{~K} \\ & 50=\left(1-\frac{\mathrm{T}_{\text {sink }}}{600}\right) \times 100 \\ & \frac{1}{2}=1-\frac{\mathrm{T}_{\text {sink }}}{600} \\ & \mathrm{~T}_{\text {Sink }}=300 \mathrm{~K} \end{aligned} $$

So temp. of sink is $${ }^{\circ} \mathrm{C}=300-2763=27^{\circ} \mathrm{C}$$

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