Question

A gas in container A is in thermal equilibrium with another gas in container B both contains equal masses of the two gases in the respective containers. Which of the following can be true? (1) $p_A{V}_A=p_B{V}_B$ (2) $p_A=p_B,V_A\ne V_B$ (3) $\frac{p_A}{V_A}=\frac{p_B}{V_B}$ (4) $p_A\ne p_B,V_A=V_B$

• A. 1, 2 and 3 are correct.
• B. 1 and 2 are correct.
• C. 2 and 4 are correct.
• D. 1 and 3 are correct.

Answer 1

Answer: (C)

According to problem mass of gases are equal so number of moles will not be equal ie, ${\mu }_A\ne {\mu }_B$
From ideal gas equation $pV=\mu RT$
$\Rightarrow$ $\frac{p_A{V}_A}{{\mu }_A}=\frac{p_B{V}_B}{{\mu }_B}$
[As temperature of the container are equal] From this relation it is clear that if
$p_A=p_B,$ then $\frac{V_A}{V_B}=\frac{{\mu }_A}{{\mu }_B}\ne 1$ ie, $V_A\ne V_B$ Similarly, if $V_A=V_B$ then $\frac{P_A}{P_B}=\frac{{\mu }_A}{{\mu }_B}\ne 1$ ie, $P_A\ne P_B$