Question

Two identical containers $A$ and $B$ having same volume of an ideal gas at the same temperature have mass of the gas as ${}^{\prime }{m}_A^{\prime }$ and ${}^{\prime }{m}_B{}^{\prime }$ respectively. $2m_A=3m_B$. 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 $B$.

• A. $2\Delta p$
• B. $3\Delta p$
• C. $\frac{2}{3}\Delta p$
• D. $\frac{4}{3}\Delta p$

Answer 1

The correct option is C $\frac{2}{3}\Delta p$

Given $2m_a=3m_b$

Isothermal expansion to double volume implies pressure is halved.

For same gas, ideal gas equation suggests pressure$\propto$ mass

Let initial pressures be $P_a$ and $P_b$ respectively.

Then $P_b=P_a\frac{m_b}{m_a}=2P_a/3$

$\Rightarrow \Delta P_b=\frac{2}{3}\Delta P_a=\frac{2}{3}\Delta p$