Two identical containers A and B having same volume of an ideal gas at the same temperature have mass of the gas as mA and mB respectively, 2mA = 3 mB. The gas in each cylinder expand isothermally to double its volume. If the change in pressure in A is \(\Delta p\), find the change in pressure in B :
Answer & explanation
Correct answer: option 4
2 mA = 3 mB
\(p_A V = \frac{m_A}{M}RT\)
\(p_B V = \frac{m_A}{m}RT = \frac{2m_A}{3 M}RT\)
So, \(\frac{p_A}{p_B} = \frac{3}{2}\)
The expansion is isothermal, so pressure will reduce to half when volume is doubled.
\(p_A - \frac{p_A}{2} = \Delta p\)
\(\Rightarrow p_A = 2 \Delta p\)
\(p_B - \frac{p_B}{2} = \frac{p_B}{2}\)
\(p_B - \frac{p_B}{2} = \frac{1}{2} \frac{2}{3} p_A\)
\(p_B - \frac{p_B}{2} = \frac{1}{3} p_A = \frac{2}{3} \Delta p\)
\(p_B = \frac{4}{3} \Delta p\)