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Mechanical Properties Of Fluids

Question
CBSEENPH11020329

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 32 V,the efficiency of the engine is

  • 0.5

  • 0.75

  • 0.99

  • 0.25

Solution

B.

0.75

because space PV to the power of straight gamma space equals space constant
TV to the power of straight gamma minus 1 end exponent space equals space Constant
rightwards double arrow space straight T subscript straight b straight V subscript straight b superscript straight gamma minus 1 end superscript space equals space space straight T subscript straight c straight V subscript straight c superscript straight gamma minus 1 end superscript
rightwards double arrow space straight T subscript straight b over straight V subscript straight c space equals space open parentheses straight V subscript straight c over straight V subscript 0 close parentheses to the power of straight gamma minus 1 end exponent space equals space open parentheses fraction numerator 32 space straight V over denominator straight V end fraction close parentheses to the power of 7 over 5 minus 1 end exponent
space equals space left parenthesis 2 to the power of 5 right parenthesis to the power of 2 over 5 end exponent
straight T subscript straight b space equals space 4 straight T subscript straight c space equals space 4
straight i. straight e. comma space 1 minus straight T subscript straight c over straight T subscript straight b space equals space 1 minus 1 fourth space equals space 3 over 4