Question

A thermodynamic process of the one-mole ideal gas is shown in the figure. The efficiency of the cyclic process ABCA will be;

• A. 25%
• B. 12.5%
• C. 50%
• D. 7.7%

Answer 1

The correct option is D 7.7%

Given,

$n=1mole$

From the given figure

Work done, $W=$ Area under the $V-P$ curve

$W=\frac{1}{2}\times (2P_0-P_0)\times (2V_0-V_0)$

$W=\frac{P_0{V}_0}{2}$. . . . .. . . .(1)

Heat supplied $Q=Q_{AB}+Q_{BC}$

$Q=n{C}_V\Delta T+n{C}_P\Delta T$

$Q=1\times C_V(2T_0-T_0)+1\times C_P(4T_0-2T_0)$

$Q=C_V{T}_0+2C_P{T}_0$

$Q=4P_0{V}_0$. . . . . . .(2)

Efficiency, $\eta =\frac{W}{Q}$

$\eta =\frac{P_0{V}_0/2}{4V_0{P}_0}\times 100$

$\eta =\frac{100}{13}=7.7$%

The correct option is D.