Question

One mole of a monoatomic ideal gas occupies two chambers of a cylinder partitioned by means of a movable piston. The walls of the cylinder as well as the piston are thermal insulators. Initially, equal amounts of gas fill both the chambers at $(P_0,V_0,T_0)$. A coil is burnt in the left chamber which causes the gas to absorb heat and expand, pushing the piston to the right. The gas in the right chamber is compressed until the pressure is $32P_0$

Choose the correct options.

• A. The final volume of the left chamber is $\frac{15V_0}{8}$.
• B. The final volume of the left chamber is $\frac{9V_0}{8}$.
• C. The work done on the gas in the right chamber is $12P_0{V}_0$.
• D. The work done on the gas in the right chamber is $\frac{9}{2}{P}_0{V}_0$

Answer 1

Answer: (A), (D)

The correct options are
A The final volume of the left chamber is $\frac{15V_0}{8}$.
D The work done on the gas in the right chamber is $\frac{9}{2}{P}_0{V}_0$

Since the compression on the right is adiabatic $P_0{V}_0^{\gamma }=P_R{V}_R^{\gamma }$
$P_0{V}_0^{\frac{5}{3}}=32P_0{V}_R^{\frac{5}{3}}$
($\because$ Monoatomic gas and given $P_R=32P_0$)
$\Rightarrow V_R=\frac{1}{8}{V}_0$ and $V_L=V_0+\frac{7}{8}{V}_0=\frac{15}{8}{V}_0$

Work done on the gas $=\frac{P_R{V}_R-P_0{V}_0}{\gamma -1}$
$P_R{V}_R=32P_0\times \frac{V_0}{8}=4P_0{V}_0$
$\therefore$ Work done $=\frac{P_0{V}_0-4P_0{V}_0}{\frac{5}{3}-1}$
$=\frac{9}{2}{P}_0{V}_0$ ($\because$ monoatomic gas)