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Question

Two identical vessels A and B with frictionless pistons conatin the same ideal gas at the same temperature and the same volume V. The masses of gas in A and B are m subscript A end subscript a n d m subscript B end subscript respectively. The gases are allowed to expand isothermally to same final volume 2 blank V. The change in pressures of the gas in A and B are found to be increment p a n d blank 1.5 blank increment p respectively. Then

  1. 9 m subscript A end subscript equals 4 m subscript B end subscript    
  2. 3 m subscript A end subscript equals 2 m subscript B end subscript    
  3. 2 m subscript A end subscript equals 3 m subscript B end subscript    
  4. 4 m subscript A end subscript equals 9 m subscript B end subscript    

The correct answer is: 9 m subscript A end subscript equals 4 m subscript B end subscript


    Let p subscript 1 end subscript a n d p subscript 2 end subscript are the initial and final pressures of the gas filled in A. Then
    p subscript 1 end subscript equals fraction numerator n subscript A end subscript R T over denominator V end fraction a n d p subscript 2 end subscript equals fraction numerator n subscript A end subscript R T over denominator 2 V end fraction
    increment p equals p subscript 2 end subscript minus p subscript 1 end subscript equals negative fraction numerator n subscript A end subscript R T over denominator 2 V end fraction
    equals negative open parentheses fraction numerator m subscript A end subscript over denominator M end fraction close parentheses fraction numerator R T over denominator 2 V end fraction…(i)
    where M is the atomic weight of the gas.
    Similarly, 1.5 increment p equals negative open parentheses fraction numerator m subscript B end subscript over denominator M end fraction close parentheses fraction numerator R T over denominator 2 V end fraction…(ii)
    Dividing Eq.(ii) by Eq. (i), we get
    1.5 equals fraction numerator m subscript B end subscript over denominator m subscript A end subscript end fraction o r fraction numerator 3 over denominator 2 end fraction equals fraction numerator m subscript B end subscript over denominator m subscript A end subscript end fraction
    or 3 m subscript A end subscript equals 2 m subscript B end subscript

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