A process in which work performed by an ideal gas is proportional to the corresponding increment of its internal energy is described as a polytropic process. If we represent work done by a polytropic process by W and increase in internal energy as $\mathrm{\Delta U}$ then

     $\mathrm{W}\propto \mathrm{\Delta U}$

or  $\mathrm{W}={\mathrm{K}}_1\mathrm{\Delta U}$   ……..(i)

For this process, it can be demonstrated that the relation between pressure and volume is given by the equation

      ${\mathrm{PV}}^{\mathrm{\eta }}={\mathrm{K}}_2\text{ (constant) }$   ……….(ii)

We know that a gas can have various values for molar specific heats. The molar specific heat 'C' for an ideal gas in polytropic process can be calculated with the help of first law of thermodynamics. In polytropic process the variation of molar specific heat 'C' with $\eta$ for a monatomic gas is plotted as in the graph shown.