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Mechanical Properties Of Fluids

Question
CBSEENPH11020256

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by PVn=constant, then n is given by (Here CP and CV are molar specific heat at constant pressure and constant volume, respectively):

  • straight n space equals straight C subscript straight p over straight C subscript straight v
  • straight n equals space fraction numerator straight C minus space straight C subscript straight p over denominator straight C minus straight C subscript straight v end fraction
  • straight n equals fraction numerator straight C subscript straight p minus straight C over denominator straight C minus straight C subscript straight v end fraction
  • straight n space equals space fraction numerator straight C minus straight C subscript straight v over denominator straight C minus straight C subscript straight p end fraction

Solution

B.

straight n equals space fraction numerator straight C minus space straight C subscript straight p over denominator straight C minus straight C subscript straight v end fraction

For the polytropic process, specific heat for an ideal gas.
straight C space equals space fraction numerator straight R over denominator 1 minus straight n end fraction space plus space straight C subscript straight v
therefore comma space fraction numerator straight R over denominator 1 minus straight n end fraction space plus straight C subscript straight v space equals space straight C
rightwards double arrow space fraction numerator straight R over denominator 1 minus straight n end fraction space equals space straight C minus straight C subscript straight v
rightwards double arrow fraction numerator straight R over denominator straight C minus straight C subscript straight v end fraction equals space 1 minus straight n space left parenthesis where comma space straight R thin space equals space straight C subscript straight p minus straight C subscript straight v right parenthesis
rightwards double arrow space fraction numerator straight C subscript straight p minus straight C subscript straight v over denominator straight C minus straight C subscript straight v end fraction space equals space 1 minus straight n
straight n space equals space 1 minus space fraction numerator straight C subscript straight p minus straight C subscript straight v over denominator straight C minus straight C subscript straight v end fraction space rightwards double arrow space straight n space equals space fraction numerator straight C minus straight C subscript straight p over denominator straight C minus straight C subscript straight v end fraction
Thus comma space number space of space moles space straight n space is space given space by space
straight n space equals space fraction numerator straight C minus straight C subscript straight p over denominator straight C minus straight C subscript straight v end fraction