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Question

The rectangle box shown in fig has a partition which can slide without friction along the length of the box. Initially each of the two chambers of the box has one mole of monatomic ideal gas (gamma =5/(c) at a pressureP subscript 0 end subscript, volumeV subscript 0 end subscript and temperatureT subscript 0 end subscript. The chamber on the left is slowly heated by an electric heater. The walls of the box and the partition are thermally insulated. The gas in the left chamber expands, pushing the partition until the final pressure in both chambers becomes (243/3(b) P subscript 0 end subscript. The final temperature of the gas in left chamber is:

  1. 63 T subscript 0 end subscript    
  2. 9 T subscript 0 end subscript    
  3. 13 T subscript 0 end subscript    
  4. 21 T subscript 0 end subscript    

The correct answer is: 13 T subscript 0 end subscript


    P subscript 0 end subscript V subscript 0 end subscript to the power of fraction numerator 5 over denominator 3 end fraction end exponent equals open parentheses fraction numerator 243 over denominator 82 end fraction close parentheses P subscript 0 end subscript V subscript R end subscript to the power of fraction numerator 5 over denominator 3 end fraction end exponent rightwards double arrow V subscript R end subscript equals fraction numerator 8 V subscript 0 end subscript over denominator 27 end fractiontherefore V subscript L end subscript equals 2 V subscript 0 end subscript minus fraction numerator 8 V subscript 0 end subscript over denominator 27 end fraction equals fraction numerator 46 V subscript 0 end subscript over denominator 27 end fraction
    From ideal gas equation rightwards double arrow T subscript L end subscript equals 13 T subscript 0 end subscript

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