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

$\frac{P_{1}}{T_{1}} + \frac{P_{2}}{T_{2}}$

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$\frac{P_{1} T_{1} + P_{2} T_{2}}{(T_{1} + T_{2})^{2}}$

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$\frac{P_{1} T_{2} + P_{2} T_{1}}{(T_{1} + T_{2})^{2}}$

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$\frac{P_{1}}{2 T_{1}} + \frac{P_{2}}{2 T_{2}}$

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Solution

The correct option is D
$\frac{P_{1}}{2 T_{1}} + \frac{P_{2}}{2 T_{2}}$

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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Similar questions

Q. Two containers of equal volume contain the same gas at different 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

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