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Question
Figure shows two vessels A and B with rigid walls containing ideal gases. The pressure, temperature and the volume are pA, TA, V in the vessel A and pB, TB, V in the vessel B. The vessels are now connected through a small tube. Show that the pressure p and the temperature T satisfy `Ρ/T = 1/2 ({P_A}/{T_A}+{P_B}/{T_B))` when equilibrium is achieved.
Solution
Let the partial pressure of the gas in chamber A and B be P'A and P'B , respectively.
Applying equation of state for gas A, we get
`{P_A V}/{T_A} = (P'_A2V)/T`
`rArr P'_A=(P_AT)/(2T_A)`
Similarly, For gas B :
`P'_B = (P_BT)/(2T_B)`
Total Pressure is the sum of the partial pressures . It is given by
P = P'A + P'B
= `(P_AT)/(2T_A) + (P_BT)/(2T_B)`
⇒ P = `T/2(P_A/T_A + P_B/T_B)`
⇒ `P/T` = `1/2 (P_A/T_A + P_B/T_B)`
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