Question

An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to ________.

Answer 1

Answer: 19.00

$W_{ABCDA}=2P_0{V}_0$
$Q_{\text{ in }}=Q_{AB}+Q_{BC}$
$Q_{AB}=nC\left(T_B-T_A\right)$
$=\frac{n3R}{2}\left(T_B-T_A\right)$
$=\frac{3}{2}\left(P_B{V}_B-P_A{V}_A\right)$
$=\frac{3}{2}\left(3P_B{V}_0=P_0{V}_0\right)=3P_0{V}_0$
$Q_{BC}=n{C}_P\left(T_C-T_B\right)$
$=\frac{n5R}{2}\left(T_C-T_B\right)$
$=\frac{5}{2}\left(P_C{V}_C-P_B{V}_B\right)$
$=\frac{5}{2}\left(6P_0{V}_0-3P_0{V}_0\right)=\frac{15}{2}{P}_0{V}_0$
$\eta =\frac{W}{Q_{\text{in }}}\times 100=\frac{2P_0{V}_0}{3P_0{V}_0+\frac{15}{2}{P}_0{V}_0}\times 100$
$\eta =\frac{400}{21}=19.04\approx 19$
$\eta =19$