Question

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

• A. Q / 4
• B. Q / 3
• C. Q / 2
• D. 2Q / 3

Answer 1

The correct option is B

Q / 3

$\because \eta =1-\frac{T_2}{T_1}=\frac{W}{Q_1}=\frac{Q_1-Q_2}{Q_1}$

where $Q_1$ = heat absorbed, $Q_2$ = heat rejected

$\Rightarrow 1-\frac{\frac{T}{3}}{T}=\frac{W}{Q_1}\Rightarrow \frac{2}{3}=\frac{W}{Q_1}=\frac{Q_1-Q_2}{Q_1}$

$\Rightarrow \frac{2}{3}=1-\frac{Q_2}{Q_1}\Rightarrow \frac{Q_2}{Q_1}=\frac{1}{3}\Rightarrow Q_2=\frac{Q_1}{3}=\frac{Q}{3}$