Question

The state of an ideal gas is changed through an isothermal process at temperature $T_o$ as shown in figure. The work done by gas in going from state B to C is double the work done by gas in going from state A to B. If the pressure in the state B is $\frac{P_o}{2}$, then pressure of the gas in state C is

• A. $\frac{P_o}{3}$
• B. $\frac{P_o}{4}$
• C. $\frac{P_o}{6}$
• D. $\frac{P_o}{8}$

Answer 1

Answer: (D)

$\frac{P_o}{8}$

Given : $P_A=P_o$ $P_B=\frac{P_o}{2}$

Let the pressure at C be $P_C$.

Workdone in isothermal process from A to B, $W_{AB}=nRT\ln (\frac{P_A}{P_B})$

$\therefore$ $W_{AB}=nRT\ln (\frac{P_o}{P_o/2})=nRT$ $\ln 2$

Workdone in isothermal process from B to C, $W_{BC}=nRT\ln (\frac{P_B}{P_C})$

$\therefore$ $W_{BC}=nRT\ln (\frac{P_o}{2P_C})$

According to question, $W_{BC}=2W_{AB}$

$\therefore$ $nRT\ln (\frac{P_o}{2P_C})=$ $2nRT$ $\ln 2$

$\ln (\frac{P_o}{2P_C})=$ $\ln 4$ $⟹\frac{P_o}{2P_C}=4$

$⟹$ $P_C=\frac{P_o}{8}$