Verified Solution • 2025–26 Session moderate

QPages 34-37: Q31: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q31 Solution: Figure shows two vessels A and B with rigid walls containing…

Figure shows two vessels A and B with rigid walls containing ideal gases. The pressure, temperature and the volume are pAp_A, TAT_A, VV in the vessel A and pBp_B, TBT_B, VV in the vessel B. The vessels are now connected through a small tube. Show that the pressure pp and the temperature TT satisfy \frac{p}{T} = \frac{1}{2} \left \frac{p_A}{T_A} + \frac{p_B}{T_B} \right) when equilibrium is achieved.

Step-by-Step Verified Solution

**Answer:** PT=12(PATA+PBTB)\frac{P}{T} = \frac{1}{2}\left(\frac{P_A}{T_A} + \frac{P_B}{T_B}\right) **Step-by-Step Explanation:** After connection, the total number of moles is conserved:
nA+nB=n=PAVRTA+PBVRTBn_A + n_B = n = \frac{P_A V}{RT_A} + \frac{P_B V}{RT_B}
The final state has volume 2V2V and temperature TT:
n=P(2V)RTn = \frac{P(2V)}{RT}
Equating and simplifying gives the result.

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