Question

An engine operates by taking $n$ moles of an ideal gas through the cycle $ABCDA$ shown in figure. The thermal efficiency of the engine is :
(Take $C_v = 1.5 \, R,$ where $R$ is gas constant)

• A. 0.24
• B. 0.15
• C. 0.32
• D. 0.08

Answer 1

Answer: (B)

$w = P_{0}V_{0}$
Heat given = $Q_{AB} = Q_{BC}$
$= nC_{V}dT_{AB} + nC_{P}dT_{BC}$
$=\frac{3}{2}\left(nRT_{B}-nRT_{A}\right)+\frac{5}{2} \left(nRT_{C} - nRT_{B}\right)$
$= \frac{3}{2}\left(2P_{0}V_{0} - P_{0}V_{0}\right)+\frac{5}{2}\left(4P_{0}V_{0} - 2P_{0}V\right)$
$= \frac{13}{2}P_{0}V_{0}$
$n = \frac{w}{Qgiven} = \frac{2}{13} = 0.15$