One gas of mole of molecules at temperature , volume , and pressure , and another gas of mole of molecules at temperature

Question

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 ______. [2026]

Smart Achievers · Accepted Answer

(2)

$n_{total} = n_{1} + n_{2}$

$P V = n R T \Rightarrow n = \frac{P V}{R T}$

$\frac{P V}{T_{final}} = \frac{P_{1} V_{1}}{T_{1}} + \frac{P_{2} V_{2}}{T_{2}}$

$T_{final} = \frac{T_{1} T_{2} P V}{P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1}}$

Solution

1 $\frac{(T_{1} + T_{2})}{2}$

2 $\frac{T_{1} T_{2} P V}{(T_{2} P_{1} V_{1} + T_{1} P_{2} V_{2})}$

3 $(T_{2} P_{1} V_{1} + T_{1} P_{2} V_{2}) (T_{1} T_{2} P V)$

4 $\frac{| T_{1} - T_{2} |}{2}$

Ans.
(2)

$n_{total} = n_{1} + n_{2}$

$P V = n R T \Rightarrow n = \frac{P V}{R T}$

$\frac{P V}{T_{final}} = \frac{P_{1} V_{1}}{T_{1}} + \frac{P_{2} V_{2}}{T_{2}}$

$T_{final} = \frac{T_{1} T_{2} P V}{P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1}}$

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Solution

Q. 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 ______. [2026]

1 (T1+T2)2

2 T1T2PV(T2P1V1+T1P2V2)

3 (T2P1V1+T1P2V2)(T1T2PV)

4 |T1-T2|2