Question

Two identical containers $A$ and $B$ having the same volume of an ideal gas at the same temperature have the mass of the gas as $m_1$ and $m_2$ respectively and $2m_1=3m_2$ . The gas in each cylinder expands isothermally to double of its volume. If the change in pressure in $A$ is $300Pa$ , then the change in pressure in $B$ is

• A. $200Pa$
• B. $300Pa$
• C. $400Pa$
• D. $500Pa$

Answer 1

Answer: (A)

$2m_1=3m_2$
$P_{1}V=\frac{m_1}{M}RTand{P}_{2}V=\frac{m_2}{M}RT=\frac{2}{3}\frac{m_1}{M}RT$
$\frac{P_1}{P_2}=\frac{3}{2}$ ………(i)
The process is isothermal $\left(P_1{V}_1=P_2{V}_2\right)$
Hence, $\Delta P_1=P_1-\frac{P_1}{2}\Rightarrow P_1=2\Delta P_1$
$\Delta P_2=P_2-\frac{P_2}{2}=\frac{P_2}{2}=\frac{1}{2}\frac{2}{3}{P}_1=\frac{P_1}{3}$
$\Delta P_2=\frac{2}{3}\Delta P_1=\frac{2}{3}.300$
$\Delta P_2=200Pa$