Question

Two flasks $R$ and $S$ of volume $V_{1}$ and $V_{2}$ contain same gas at pressure $P_{1}$ and $P_{2}$ respectively at the same temperature. Pressure of the gas when the flasks $R$ and $S$ are connected by a tube of negligible volume is

• A. $\frac{P_{1} V_{1}+P_{2} V_{2}}{V_{1}+V_{2}}$
• B. $\frac{P_{1} V_{1}+P_{2} V_{2}}{2\left(V_{1}+V_{2}\right)}$
• C. $\frac{P_{1} V_{2}+P_{2} V_{1}}{V_{1}+V_{2}}$
• D. $\frac{\left(P_{1}+P_{2}\right)\left(V_{1}+V_{2}\right)}{\left(V_{1}+2 V_{2}\right)}$

Answer 1

Answer: (A)

Number of moles of gas in two flasks are
$n_{1}=\frac{P_{1} V_{1}}{R T}$ and
$n_{2}=\frac{P_{2} V_{2}}{R T} $
$\because n=n_{1}+n_{2}$
$\therefore P=\frac{\left(n_{1}+n_{2}\right) R T}{V_{1}+V_{2}}$
$=\frac{P_{1} V_{1}+P_{2} V_{2}}{V_{1}+V_{2}}$