Question

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)

Answer 1

Where the molar heat capacity remains constant, Where the pressure P and volume V

So Pvn = constant

C=Cv+R/1−η

The specific heat for a polytropic gas is an ideal gas

Here Cp and Cv are molar specific heat at the constant pressure and constant volume, respectively

=> 1−n=R/C−Cv

n=1−R/C−Cv ( Where R = Cp-Cv)

=C−(Cv+R)/C−Cv

=C−Cp/C−Cv gives the number of moles n