Two identical vessels $A$ and $B$ with frictionless pistons contain the same ideal gas at the same…
Two identical vessels $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The masses of gas in $A$ and $B$ and $m_A$ and $m_B$, respectively. The gases are allowed to expand isothermally to the same final volume $2 V$. The change in pressures of the gas in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$, respectively. Then
$9 m_A=4 m_B$
$3 m_A=2 m_B$
$2 m_A=3 m_B$
$4 m_A=9 m_B$
Solution
Let $p_1$ and $p_2$ are the initial and final pressures of the gas filled in $A$. Then
$
p_1=\frac{\mu_{\mathrm{A}} R T}{V} \text { and } P_2=\frac{\mu_A R T}{2 V}
$
Dividing Eq. (ii) by (i), we get
$\begin{aligned} 1.5 & =\frac{m_B}{m_A} \\ \text { or } \quad \frac{3}{2} & =\frac{m_B}{m_A} \\ \text { or } \quad 3 m_A & =2 m_B .\end{aligned}$
