Question

A Carnot engine used first an ideal monoatomic gas and then an ideal diatomic gas. If the source and sink temperature are ${411}^{\circ }C$ and ${69}^{\circ }C$ respectively and the engine extracts 1000 J of heat in each cycle, then area enclosed by $pV$ diagram is

• A. 100 J
• B. 300 J
• C. 500 J
• D. 700 J

Answer 1

Answer: (C)

500 J

Efficiency of Carnot engine does not depend upon the nature of gas.
Here, $T_1={411}^{\circ }C=684K$
and $T_2={69}^{\circ }C=342K$
Moreover, $Q_1=1000J$
Area of p-V diagram $=W=Q_1\left(\frac{T_1-T_2}{T_1}\right)$
$=1000\times \left(\frac{684-342}{684}\right)$
$=500J$