One gas of n₁ mole of molecules at temperature T₁, volume V₁, and pressure P₁, and another gas of n₂ mole of molecules at temperature T₂, volume V₂, and pressure P₂, are mixed resulting in pressure P and volume V of the mixture. The temperature of the mixture is ______. (a) ((T₁+T₂))/(2) (b) (T₁T₂PV)/(T₂P₁V₁+T₁P₂V₂) (c) ((T₂P₁V₁+T₁P₂V₂))/(T₁T₂PV) (d) ([T₁-T₂])/(2)

Answer: (b). Total moles are conserved: n = n₁ + n₂, with n = PV/RT. PV/RT = (P₁V₁)/(RT₁) + (P₂V₂)/(RT₂) T = (PV)/(P₁V₁/T₁ + P₂V₂/T₂) = (T₁T₂PV)/(T₂P₁V₁ + T₁P₂V₂) So the answer is (b).

One gas of n₁ mole of molecules at temperature T₁, volume V₁, and… | JEE Main 2026 (4 Apr, Shift 1)

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Degrees of Freedom & Internal Energy

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 ______.

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Answer: (b)

Total moles are conserved: $n = n_1 + n_2$ , with $n = \frac{PV}{RT}$ .
$\frac{PV}{RT} = \frac{P_1V_1}{RT_1} + \frac{P_2V_2}{RT_2}$
$T = \frac{PV}{P_1V_1/T_1 + P_2V_2/T_2} = \frac{T_1T_2PV}{T_2P_1V_1 + T_1P_2V_2}$
So the answer is (b).

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