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Thermodynamics

Question
CBSEENPH11020387

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1 and contains ideal gas at pressure P1 and temperature T1. The other chamber has volume V2 and contains ideal gas at pressure P2 and temperature T2. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

  • fraction numerator straight T subscript 1 straight T subscript 2 space left parenthesis straight P subscript 1 straight V subscript 1 space plus space straight P subscript 2 straight V subscript 2 right parenthesis over denominator straight P subscript 1 straight V subscript 1 straight T subscript 2 space plus space straight P subscript 2 straight V subscript 2 straight T subscript 1 end fraction
  • fraction numerator left parenthesis straight P subscript 1 straight V subscript 1 space straight T subscript 1 plus space straight P subscript 2 straight V subscript 2 straight T subscript 2 right parenthesis over denominator straight P subscript 1 straight V subscript 1 space plus space straight P subscript 2 straight V subscript 2 end fraction
  • fraction numerator left parenthesis straight P subscript 1 straight V subscript 1 space straight T subscript 2 plus space straight P subscript 2 straight V subscript 2 straight T subscript 1 right parenthesis over denominator straight P subscript 1 straight V subscript 1 space plus space straight P subscript 2 straight V subscript 2 end fraction
  • fraction numerator straight T subscript 1 straight T subscript 2 space left parenthesis straight P subscript 1 straight V subscript 1 space plus space straight P subscript 2 straight V subscript 2 right parenthesis over denominator straight P subscript 1 straight V subscript 1 straight T subscript 1 space plus space straight P subscript 2 straight V subscript 2 straight T subscript 2 end fraction

Solution

A.

fraction numerator straight T subscript 1 straight T subscript 2 space left parenthesis straight P subscript 1 straight V subscript 1 space plus space straight P subscript 2 straight V subscript 2 right parenthesis over denominator straight P subscript 1 straight V subscript 1 straight T subscript 2 space plus space straight P subscript 2 straight V subscript 2 straight T subscript 1 end fraction