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An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $V_1$ and contains ideal gas at pressure $P_1$ and temperature $T_1$ . The other chamber has volume $V_2$ and contains ideal gas at pressure $P_2$ and temperature $T_2$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be
  • A$\frac{{{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)}}{{{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}}}$
  • B$\;\frac{{{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)}}{{{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}}}$
  • C$\;\frac{{\left( {{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}} \right)}}{{{P_1}{V_1} + {P_2}{V_2}}}$
  • D$\;\frac{{\left( {{P_1}{V_{1{T_2}}} + {P_2}{V_2}{T_1}} \right)}}{{{P_1}{V_1} + {P_2}{V_2}}}$
AIEEE 2008, Medium
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