The ratio of pressure of the same gas in two containers is \(\frac{n_1T_1}{n_2T_2}\) where n₁ and n₂ are the number of moles and T₁ and T₂ are respective temperatures. If the two containers are now joined find the ratio of pressure to the temperature : 

\(\frac{P_1T_2 + P_2T_1}{2T_1T_2}\)

Given : \(\frac{P_1}{P_2} = \frac{n_1 T_1}{n_2 T_2}\)

P \(\propto \) nT.

It implies that volume of both containers is same. After mixing.

P(2V) = (n₁ + n₂)RT

P(2V) = (\(\frac{P_1V}{RT_1} + \frac{P_2V}{RT_2}\))Rt

\(\frac{P}{T} = \frac{1}{2} (\frac{P_1}{T_1} + \frac{P_2}{T_2})\)

\(\frac{P}{T} = \frac{1}{2} (\frac{P_1T_2 + P_2T_1}{T_1T_2})\)