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(D) For the first container,the ideal gas equation is $P_1V = n_1RT_1$,so $n_1 = \frac{P_1V}{RT_1}$.For the second container,the ideal gas equation is

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$\frac{P_1}{2T_1} + \frac{P_2}{2T_2}$

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(D) For the first container,the ideal gas equation is $P_1V = n_1RT_1$,so $n_1 = \frac{P_1V}{RT_1}$.For the second container,the ideal gas equation is $P_2V = n_2RT_2$,so $n_2 = \frac{P_2V}{RT_2}$.When the vessels are joined,the total volume becomes $2V$ and the total number of moles is $n = n_1 + n_2$.The final state is given by $P(2V) = (n_1 + n_2)RT$.Substituting the values of $n_1$ and $n_2$:$P(2V) = \left( \frac{P_1V}{RT_1} + \frac{P_2V}{RT_2} \right) RT$$2PV = \left( \frac{P_1}{T_1} + \frac{P_2}{T_2} \right) V T$Dividing both sides by $2VT$:$\frac{P}{T} = \frac{1}{2} \left( \frac{P_1}{T_1} + \frac{P_2}{T_2} \right) = \frac{P_1}{2T_1} + \frac{P_2}{2T_2}$.

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 $P/T$ is equal to

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