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 mA and that in B is mB. 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 :
Answer & explanation
Correct answer: option 3
- 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 : nB = 1.5nA
\(\Rightarrow\) 2 nB = 3 nA
\(\Rightarrow\) 2 mB = 3 mA