Two thermally insulated vessels 1 and 2 are filled with air at temperature $(T_{1,} T_{2})$ ,volume $(V_{1,} V_{2})$ and pressure $(P_{1,} P_{2})$ respectively. If the valve joining the two vessel is opened , the temperature inside the vessel at equilibrium will be

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$(T_{1} + T_{2}) / 2$

$T_{1} T_{2} (P_{1} V_{1} + P_{2} V_{2}) / (P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1})$

$(T_{1}, T_{2})$

$T_{1} T_{2} (P_{1} V_{1} + P_{2} V_{2}) / (P_{1} V_{1} T_{1} + P_{2} V_{2} T_{2})$

answer is C.

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Detailed Solution

$\begin{array}{l} n = n_{1} + n_{2} \\ \frac{P_{1} V_{1} + P_{2} V_{2}}{{RT}_{mx}} = \frac{P_{1} V_{1}}{{RT}_{1}} + \frac{P_{2} V_{2}}{{RT}_{2}} \\ \Rightarrow T_{mix} = \frac{T_{1} T_{2} (P_{1} V_{1} + P_{2} V_{2})}{P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1}} \end{array}$