Physics-
General
Easy

Question

In the following P-V diagram two adiabatics cut two isothermals at temperatures T1 and T2 (fig.). The value of fraction numerator V subscript a end subscript over denominator V subscript d end subscript end fraction will be

  1. fraction numerator V subscript b end subscript over denominator V subscript c end subscript end fraction    
  2. fraction numerator V subscript c end subscript over denominator V subscript b end subscript end fraction    
  3. fraction numerator V subscript d end subscript over denominator V subscript a end subscript end fraction    
  4. V subscript b end subscript V subscript c end subscript    

The correct answer is: fraction numerator V subscript b end subscript over denominator V subscript c end subscript end fraction


    For adiabatic process T subscript 1 end subscript V subscript b end subscript superscript gamma minus 1 end superscript= Constant
    For bc curve T subscript 1 end subscript V subscript b end subscript superscript gamma minus 1 end superscript equals T subscript 2 end subscript V subscript c end subscript superscript gamma minus 1 end superscript or fraction numerator T subscript 2 end subscript over denominator T subscript 1 end subscript end fraction equals open parentheses fraction numerator V subscript b end subscript over denominator V subscript c end subscript end fraction close parentheses to the power of gamma minus 1 end exponent (i)
    For ad curve T subscript 1 end subscript V subscript a end subscript superscript gamma minus 1 end superscript equals T subscript 2 end subscript V subscript d end subscript superscript gamma minus 1 end superscript or fraction numerator T subscript 2 end subscript over denominator T subscript 1 end subscript end fraction equals open parentheses fraction numerator V subscript a end subscript over denominator V subscript d end subscript end fraction close parentheses to the power of gamma minus 1 end exponent (ii)
    From equation (i) and (ii) fraction numerator V subscript b end subscript over denominator V subscript c end subscript end fraction equals fraction numerator V subscript a end subscript over denominator V subscript d end subscript end fraction

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