An ideal gas $$(C_p/C_v = \gamma)$$ is taken through a process in which the pressure and the volume vary as $$P= aV^b$$. Find the value of $$b$$ for which the specific heat capacity in the process is zero.
For polytropic process, $$PV^x=constant$$
Specific heat capacity, C=$$\dfrac{R}{1-x} +\dfrac{R}{\gamma - 1}$$
Given
$$C=0$$ $$\Rightarrow x=\gamma$$
Here, $$b=-x=-\gamma$$
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