First slide

Heat engine

Question

A Camot engine absorbs an amount Q of heat from a reservoir at an absolute temperature T and rejects heat to a sink at a temperature of $\frac{T}{3}$ . The amount of heat rejected is

Moderate

A

$\frac{Q}{4}$
B

$\frac{Q}{3}$
C

$\frac{Q}{2}$
D

$\frac{2 Q}{3}$

Solution

$∴ η = 1 - \frac{T_{2}}{T_{1}} = \frac{W}{Q_{1}}$
where $Q_{1} = heat absorbed, Q_{2} = heat rejected$
$\Rightarrow 1 - \frac{\frac{T}{3}}{T} = \frac{W}{Q_{1}} \Rightarrow \frac{2}{3} = \frac{W}{Q_{1}} = \frac{Q_{1} - Q_{2}}{Q_{1}}$
$\Rightarrow \frac{2}{3} = 1 - \frac{Q_{2}}{Q_{1}} \Rightarrow \frac{Q_{2}}{Q_{1}} = \frac{1}{3} \Rightarrow Q_{2} = \frac{Q_{1}}{3} = \frac{Q}{3}$

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