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Ideal Gas Equation

Two identical...

Question

Two identical containers joined by a small pipe initially contain same gas at pressure $P$ , and absolute temperature $T_{o}$ . One container is now maintained at the same temperature while the other is heated to $2 T_{o}$ . The common pressure of the gas will be

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Solution

Two identical containers means
$V_{1} P$ and $T$ same
for ideal gas equation $p V = n R T$
$n = \frac{P V}{R T}$ where $n$ is no. of mole,s
$n_{1} + n_{2} = n_{1}^{'} + n_{2}^{'}$ ( $n$ =constant)
$\begin{matrix} \frac{P v}{R T_{0}} + \frac{P v}{R T_{0}} = \frac{P^{'} v}{R T_{0}} + \frac{P^{'} v}{R 2 T_{0}} \frac{2 P v}{R T_{0}} = \frac{P^{'} v}{R T_{0}} [\frac{1}{T_{0}} + \frac{1}{2 T_{0}}] \frac{2 P v}{R T_{0}} = \frac{P^{'} v}{R T_{0}} [1 + \frac{1}{2}] P = P^{'} [\frac{3}{2}] P^{'} = \frac{4 P}{3} \end{matrix}$

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