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  4. The bulk modulus of a gas is defined as B = - Vdp / d V. For an adiabatic process the variation of B is proportional to pn . For an ideal gas n is

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Q. The bulk modulus of a gas is defined as $B = - Vdp / d V.$ For an adiabatic process the variation of $B$ is proportional to $p^n$ . For an ideal gas $n$ is

KVPYKVPY 2013Kinetic Theory

Solution:

Adiabatic bulk modulus for an ideal gas is
$K=\frac{dp}{-dV/ V}=-V\left(\frac{dp}{dV}\right) $
$= \gamma p \cdots\left(i\right)$
Now given,
$K \propto p^{n} \cdots\left(ii\right)$
$\therefore $ From Eqs. $\left(i\right)$ and $\left(ii\right),$ we have
$\Rightarrow n=1$