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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 work done on the gas in the right chamber is

  1. fraction numerator 9 over denominator 2 end fraction P subscript 0 end subscript V subscript 0 end subscript    
  2. negative fraction numerator 9 over denominator 2 end fraction P subscript 0 end subscript V subscript 0 end subscript    
  3. fraction numerator 13 over denominator 2 end fraction P subscript 0 end subscript V subscript 0 end subscript    
  4. fraction numerator 17 over denominator 2 end fraction P subscript 0 end subscript V subscript 0 end subscript    

The correct answer is: fraction numerator 9 over denominator 2 end fraction P subscript 0 end subscript V subscript 0 end subscript


    Work done on the gas=blank fraction numerator P subscript R end subscript V subscript R end subscript minus P subscript 0 end subscript V subscript 0 end subscript over denominator gamma minus 1 end fraction equals fraction numerator 4 P subscript 0 end subscript V subscript 0 end subscript minus P subscript 0 end subscript V subscript 0 end subscript over denominator 5 divided by 3 minus 1 end fraction equals fraction numerator 9 over denominator 2 end fraction P subscript 0 end subscript V subscript 0 end subscript

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    text (Given  end text open alpha subscript text lras  end text end subscript equals 1.8 cross times 10 to the power of negative 5 end exponent degree C to the power of negative 1 end exponent comma alpha subscript text sleel  end text end subscript equals 1.2 cross times 10 to the power of negative 5 end exponent blank to the power of ring operator end exponent C to the power of negative 1 end exponent comma Y subscript text steel  end text end subscript equals 2 cross times 10 to the power of 11 end exponent N m to the power of negative 2 end exponent comma Y subscript text bas  end text end subscript equals 1.7 cross times 10 to the power of 7 end exponent N m to the power of negative 2 end exponent close parentheses

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