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General
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Question

Figure shows the variation of the internal energy U with density r of one mole of an ideal monatomic gas for thermodynamic cycle ABCA. Here process AB is a part of rectangular hyperbola :-

  1. process AB is isothermal & net work in cycle is done by gas    
  2. process AB is isobaric & net work in cycle is done by gas    
  3. process AB is isobaric & net work in cycle is done on the gas    
  4. process AB is adiabatic & net work in cycle is done by gas    

The correct answer is: process AB is isobaric & net work in cycle is done by gas


    For the process AB: Ur = constant (hyperbola)
    U equals fraction numerator 3 over denominator 2 end fraction R T (monoatomic ideal gas); fraction numerator 3 over denominator 2 end fraction rho R T equals text  constant end text
    Comparing it with ideal gas equation P equals open parentheses fraction numerator 1 over denominator M end fraction close parentheses rho R T rightwards double arrow P text  is constant. end text
    P-V graph for the cycle is Thus work done in cycle is positive

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