Two identical containers A and B have frictionless pistons. They contain the same volume of an ideal gas at the same temperature. The mass of the gas in A in m_A and that in B is m_B. The gas in each cylinder is now allowed to expand isothermally to double the initial volume. The change in the pressure in A and B, respectively, is \(\Delta p\) and 1.5 \(\Delta p\). Then : 

3 m_A = 2 m_B

• For the gas in container A : 

\(\Delta P = (P_A)_{final} - (P_A)_{initial}\)

\(\Delta P = \frac{n_A RT}{2V} - \frac{n_A RT}{V}\)

\(\Delta P = - \frac{n_A RT}{2V}\) ... (i)

• For the gas in container B :

\(1.5 \Delta P = (P_B)_{final} - (P_B)_{initial}\)

\(1.5 \Delta P = \frac{n_B RT}{2V} - \frac{n_B RT}{V}\)

\(1.5 \Delta P = - \frac{n_B RT}{2V}\) ... (ii)

From eq : (i) and (ii), we get : n_B = 1.5n_A

\(\Rightarrow\) 2 n_B = 3 n_A

\(\Rightarrow\) 2 m_B = 3 m_A