Question

Helium gas goes through a cycle $ABC$ (consisting of two isochoric and isobaric lines) as shown in figure. Efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)

• A. $15.4\%$
• B. $9.1\%$
• C. $10.5\%$
• D. $12.5\%$

Answer 1

The correct option is A $15.4\%$

$\eta =\frac{Workdonebygas}{Heatgiventogas}$

Work done by gas = Area under curve= $P_0{V}_0$
Heat given by gas= Heat given by gas from $A$ to $B$ + Heat given by gas from $B$ to $C$

Heat given by gas= $n{C}_v\Delta T$ + $n{C}_p\Delta T$
$C_p$ and $C_v$ for monoatomic gas is $\frac{5R}{2}$ and $\frac{3R}{2}$ respectively.
Heat given by gas= $\frac{3}{2}{P}_0{V}_0$ + $5P_0{V}_0$

$\eta =\frac{P_0{V}_0}{\frac{3}{2}{P}_0{V}_0+5P_0{V}_0}=15.4$