Two chambers (V_1, P_1, T_1) and (V_2, P_2, T_2) are separated by an insulating partition. If the partition is removed, the final equilibrium temperat - Physics MCQ AIEEE 2026 | ExamTest.live

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Two chambers (V_{1}, P_{1}, T_{1}) and (V_{2}, P_{2}, T_{2}) are separated by an insulating partition. If the partition is removed, the final equilibrium temperature is:

A $\frac{T _{1} T _{2} ( P _{1} V _{1} + P _{2} V _{2} )}{P _{1} V _{1} T _{2} + P _{2} V _{2} T _{1}}$
B $\frac{P _{1} V _{1} T _{1} + P _{2} V _{2} T _{2}}{P _{1} V _{1} + P _{2} V _{2}}$
C $\frac{P _{1} V _{1} T _{2} + P _{2} V _{2} T _{1}}{P _{1} V _{1} + P _{2} V _{2}}$
D $\frac{T _{1} T _{2} ( P _{1} V _{1} + P _{2} V _{2} )}{P _{1} V _{1} T _{1} + P _{2} V _{2} T _{2}}$

Solution & Step-by-step Explanation

Total internal energy U = U_{1} + U_{2} .For an ideal gas, U = n C_{v} T = \frac{f}{2} n RT = \frac{f}{2} P V .Final internal energy U_{f} = \frac{f}{2} (n_{1} + n_{2}) R T_{f} = \frac{f}{2} (P_{1} V_{1} + P_{2} V_{2}) .Number of moles n_{1} = \frac{P _{1} V _{1}}{R T _{1}} and n_{2} = \frac{P _{2} V _{2}}{R T _{2}} . (n_{1} + n_{2}) R T_{f} = P_{1} V_{1} + P_{2} V_{2} (\frac{P _{1} V _{1}}{T _{1}} + \frac{P _{2} V _{2}}{T _{2}}) T_{f} = P_{1} V_{1} + P_{2} V_{2} T_{f} (\frac{P _{1} V _{1} T _{2} + P _{2} V _{2} T _{1}}{T _{1} T _{2}}) = P_{1} V_{1} + P_{2} V_{2} T_{f} = \frac{( P _{1} V _{1} + P _{2} V _{2} ) T _{1} T _{2}}{P _{1} V _{1} T _{2} + P _{2} V _{2} T _{1}}

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Two chambers (V_{1}, P_{1}, T_{1}) and (V_{2}, P_{2}, T_{2}) are separated by an insulating partition. If the partition is removed, the final equilibrium temperature is:

\frac{T _{1} T _{2} ( P _{1} V _{1} + P _{2} V _{2} )}{P _{1} V _{1} T _{2} + P _{2} V _{2} T _{1}}

\frac{P _{1} V _{1} T _{1} + P _{2} V _{2} T _{2}}{P _{1} V _{1} + P _{2} V _{2}}

\frac{P _{1} V _{1} T _{2} + P _{2} V _{2} T _{1}}{P _{1} V _{1} + P _{2} V _{2}}

\frac{T _{1} T _{2} ( P _{1} V _{1} + P _{2} V _{2} )}{P _{1} V _{1} T _{1} + P _{2} V _{2} T _{2}}

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