Two containers of equal volume contain the same gas at pressures $P_{1}$ and $P_{2}$ and absolute temperatures $T_{1}$ and $T_{2}$ respectively. On joining the vessels, the gas reaches a common pressure P and common temperature T. The ratio $\frac{P}{T}$ is equal to

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Solution

The correct option is D

As the gas does not escape the number of moles of the gas is constant.

$n_{1} = \frac{P_{1} V_{1}}{R T_{1}}; n_{2} = \frac{P_{2} V_{2}}{R T_{2}} after joining n_{1} + n_{2} = \frac{P (V_{1} + V_{2})}{R T} H e n c e, \frac{P_{1} V_{1}}{R T_{1}} + \frac{P_{2} V_{2}}{R T_{2}} = \frac{P (V_{1} + V_{2})}{R T} \Rightarrow \frac{P_{1}}{2 T_{1}} + \frac{P_{2}}{2 T_{2}} = \frac{P}{T} (a s V_{1} = V_{2})$

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Two containers of equal volume contain the same gas at pressures $P_{1}$ and $P_{2}$ and absolute temperatures $T_{1}$ and $T_{2}$ respectively. On joining the vessels, the gas reaches a common pressure P and common temperature T. The ratio $\frac{P}{T}$ is equal to