Q 11-12-031JEE MainJEE Main 2026 (4 Apr, Shift 1)Medium
One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure $P$ and volume $V$ of the mixture. The temperature of the mixture is ______.
Answer: (B) $\dfrac{T_1T_2PV}{T_2P_1V_1 + T_1P_2V_2}$
The number of moles is conserved: $\dfrac{PV}{RT} = \dfrac{P_1V_1}{RT_1} + \dfrac{P_2V_2}{RT_2}$.
$$T = \frac{PV}{\frac{P_1V_1}{T_1} + \frac{P_2V_2}{T_2}} = \frac{T_1T_2PV}{T_2P_1V_1 + T_1P_2V_2}$$
Solution by Sreeraj P, M.Sc Physics