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An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $\dpi{100} V_{1}$ and contains ideal gas at pressure $\dpi{100} P_{1}$ and temperature $\dpi{100} T_{1}$ . The other chamber has volume $\dpi{100} V_{2}$ and contains ideal gas at pressure $\dpi{100} P_{2}$ and temperature $\dpi{100} T_{2}$ . If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

• Option 1)

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

• Option 2)

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

• Option 3)

$\frac{P_{1}V_{1}T_{1}+P_{2}V_{2}T_{2}}{P_{1}V_{1}+P_{2}V_{2}}$

• Option 4)

$\frac{P_{1}V_{1}T_{2}+P_{2}V_{2}T_{1}}{P_{1}V_{1}+P_{2}V_{2}}$

As we learnt in  Change in internal energy for cyclic process -   - wherein Since in a cyclic process initial and final state is same.     Option 1) This option is incorrect. Option 2) This option is correct. Option 3) This option is incorrect. Option 4) This option is incorrect.
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