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Standard XI

Physics

Carnot Cycle

A Carnot engi...

Question

A Carnot engine absorbs $Q_{1}$ amount of heat from a reservoir at an absolute temperature $T$ and rejects heat to a sink at a temperature of $T / 3$ . The amount of heat rejected is

Q_{1} / 4

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Q_{1} / 3

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Q_{1} / 2

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2 Q_{1} / 3

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Solution

The correct option is B $Q_{1} / 3$
$Q_{1} = W + Q_{2}$
$η = \frac{W}{Q_{1}}$
$η = 1 - \frac{Q_{2}}{Q_{1}}$
For reversible engine Q depends only on temperature.
So, $η = 1 - \frac{T_{2}}{T_{1}}$

$η = 1 - \frac{Q_{2}}{Q_{1}} = 1 - \frac{T_{2}}{T_{1}}$
$⟹ Q_{2} = \frac{Q_{1}}{3}$

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For reversible engine Q depends only on temperature.
So, $η = 1 - \frac{T_{2}}{T_{1}}$

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