Two containers of equal volume contain identical gases at pressures P1 and P2 and absolute temperatures T1 and T2 respectively. The vessels are joined and the gas reaches a common pressure P and a common temperature T. Then

P = P 1 T 2 + P 2 T 1 T 1 2 − T 2 2 T

P = P 1 T 2 + P 2 T 1 T 1 2 + T 2 2 T

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Two containers of equal volume contain identical gases at pressures P₁ and P₂ and absolute temperatures T₁ and T₂ respectively. The vessels are joined and the gas reaches a common pressure P and a common temperature T. Then

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$P = (\frac{P_{1} T_{2} + P_{2} T_{1}}{T_{1}^{2} - T_{2}^{2}}) T$

$P = (\frac{P_{1}}{T_{1}} + \frac{P_{2}}{T_{2}}) T$

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

$P = \frac{1}{2} (\frac{P_{1}}{T_{1}} + \frac{P_{2}}{T_{2}}) T$

answer is B.

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Detailed Solution

Since P₁V = n₁RT₁
and P₂V = n₂RT₂
After joining the vessels we have
$P (2 V) = (n_{1} + n_{2}) RT$
$\begin{array}{l} \Rightarrow P (2 V) = (\frac{P_{1} V}{{RT}_{1}} + \frac{P_{2} V}{{RT}_{2}}) RT \\ \Rightarrow P = \frac{1}{2} (\frac{P_{1}}{T_{1}} + \frac{P_{2}}{T_{2}}) T \end{array}$

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