Question

An ideal gas $(\frac{C_p}{C_v}=\gamma )$ is taken through a process in which the pressure and the volume vary as $P=a{V}^b$. The value of b for specific heat capacity as zero is

• A. $2\gamma$
• B. $0$
• C. $-\gamma$
• D. $-1$

Answer 1

The correct option is C $-\gamma$

Given that $P=a{V}^b$
or $P{V}^{-b}=a$
Comparing with $P{V}^r=constant$, we have
$r=-b$
We know that molar specific heat $C=C_v-\frac{R}{r-1}$
$\therefore 0=\frac{R}{\gamma -1}-\frac{R}{-b-1}$
or $b=-\gamma$