Question

A Carnot engine absorbs $1000 \, J$ of heat energy from a reservoir at $127 \, ^\circ C$ and rejects $600 \, J$ of heat energy during each cycle. The efficiency of the engine and temperature of the sink will be

• A. $70\%$ and $-10^\circ C$
• B. $50\%$ and $-20^\circ C$
• C. $40\%$ and $-33^\circ C$
• D. $20\%$ and $-43^\circ C$

Answer 1

Answer: (C)

$Q_{1}=1000 \, J$
$Q_{2}=600$
$\eta=1-\frac{Q_{2}}{Q_{1}}$
$=40\%$
$\frac{T_{1}}{T_{2}}=\frac{Q_{1}}{Q_{2}}$
$\frac{400}{T_{2}}=\frac{1000}{600}$
$T_{2}=240K-273=-33 \, ^\circ C$