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General
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Question

One mole of a monoatomic ideal gas occupies two chambers of a cylinder partitioned by means of a movable piston. The walls of the cylinder as well as the piston are thermal insulators. Initially equal amounts of gas fill both the chambers at open parentheses P subscript 0 end subscript comma V subscript 0 end subscript comma T subscript 0 end subscript close parentheses A coil is burnt in the left chamber which absorbs heat and expands, pushing the piston to the right. The gas on the right chamber is compressed until to pressure becomes 32 P subscript 0 end subscript. The final volume of left chamber is

  1. fraction numerator V subscript 0 end subscript over denominator 8 end fraction    
  2. fraction numerator 15 over denominator 8 end fraction V subscript 0 end subscript    
  3. fraction numerator 7 over denominator 8 end fraction V subscript 0 end subscript    
  4. fraction numerator 9 over denominator 8 end fraction V subscript 0 end subscript    

The correct answer is: fraction numerator 15 over denominator 8 end fraction V subscript 0 end subscript


    Since the compression on the right is adiabatic so P subscript 0 end subscript V subscript 0 end subscript superscript gamma end superscript equals P subscript R end subscript V subscript R end subscript superscript gamma end superscript
    rightwards double arrow P subscript 0 end subscript V subscript 0 end subscript superscript 5 divided by 3 end superscript equals 32 P subscript 0 end subscript V subscript R end subscript superscript 5 divided by 3 end superscript rightwards double arrow V subscript R end subscript equals fraction numerator V subscript 0 end subscript over denominator 8 end fraction rightwards double arrow V subscript L end subscript equals V subscript 0 end subscript plus fraction numerator 7 over denominator 8 end fraction V subscript 0 end subscript equals fraction numerator 15 over denominator 8 end fraction V subscript 0 end subscript

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