Question

A partition divides a container having insulated walls into two compartments I and II. The same gas is filled in the two compartments whose initial parameters are given in figure. The partition is a conducting wall which can move freely without friction. Which of the following statements is/are correct with reference to teh final equilibrium position?

• A. The pressure in the two compartments are equal
• B. Volume of the compartment I is $\frac{3V}{5}$
• C. Volume of the compartment II is $\frac{12V}{5}$
• D. Final pressure I in compartment I is $\frac{5P}{3}$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A The pressure in the two compartments are equal
B Volume of the compartment I is $\frac{3V}{5}$
C Volume of the compartment II is $\frac{12V}{5}$
D Final pressure I in compartment I is $\frac{5P}{3}$

The pressure in the two components will be equal because the wall has to be at rest and it is not accelerating.

Let the volume on the left side is $x$ and the volume on the right side will be $3V-x$ and the final pressure in component I is $P_1$.

The expression for the left side is given as,

$P_1\times x=PV$ (1)

The expression for the right side is given as,

$P_1\times \left(3V-x\right)=2P\times 2V$ (2)

Dividing equation (1) by equation (2), we get

$\left(3V-x\right)=4x$

$x=\frac{3V}{5}$

The volume of the second compartment is,

$3V-x=3V-\frac{3V}{5}$

=$\frac{12V}{5}$

The final pressure is given as,

$P_1\times \frac{3V}{5}=PV$

$P_1=\frac{5P}{3}$

Thus, the pressure in the two components are equal, the volume in compartment I is $\frac{3V}{5}$, the volume in compartment II is $\frac{12V}{5}$ and the final pressure in compartment I is $\frac{5P}{3}$.