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JEE Main 2008
Exam
JEE Main
Year
2008
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2008 · Physics · Kinetic Theory of Gases

An insulated container of gas has two chambers separated by an...

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1V_1 and contains ideal gas at pressure P1P_1 and temperature T1T_1. The other chamber has volume V2V_2 and contains ideal gas at pressure P2P_2 and temperature T2T_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

Options

  1. AT1T2(P1V1+P2V2)P1V1T2+P2V2T1\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}
  2. BP1V1T1+P2V2T2P1V1+P2V2\frac{P_1 V_1 T_1+P_2 V_2 T_2}{P_1 V_1+P_2 V_2}
  3. CP1V1T2+P2V2T1P1V1+P2V2\frac{P_1 V_1 T_2+P_2 V_2 T_1}{P_1 V_1+P_2 V_2}
  4. DT1T2(P1V1+P2V2)P1V1T1+P2V2T2\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}

Correct answer

A. T1T2(P1V1+P2V2)P1V1T2+P2V2T1\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}

Step-by-step solution

U=U1+U2T=(P1V1+P2V2)T1T2(P1V1T2+P2V2T1)\begin{aligned}& U=U_1+U_2 \\ & T=\frac{\left(P_1 V_1+P_2 V_2\right) T_1 T_2}{\left(P_1 V_1 T_2+P_2 V_2 T_1\right)} \end{aligned}
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