AIIMS2018Physics-Thermodynamics

AIIMS 2018 Physics Carnot Engine MCQ Question

Type: MCQ-numerical-Medium-Class 11

A Carnot engine whose efficiency is 50% has an exhaust temperature of 500 K500\text{ K}. If the efficiency is to be 60% with the same intake temperature, the exhaust temperature must be

A

800 K800\text{ K}

B

200 K200\text{ K}

C

400 K400\text{ K}

D

600 K600\text{ K}

Correct Answer

Option C

Detailed Explanation

The efficiency of a Carnot engine is calculated using the formula η = 1 - (T₂/T₁), where T₁ is the temperature of the hot reservoir and T₂ is the temperature of the cold reservoir. In this case, substituting T₁ = 1000 K and T₂ = 500 K yields η = 1 - (500 K / 1000 K) = 0.5 or 50%. Since option C correctly represents this efficiency, it is the right choice. The other options are not applicable as they do not provide relevant values or calculations related to the efficiency of the Carnot engine.

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