Question:
For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $\gamma$ is the ratio of specific heats):
Correct Option: 1
Solution:
$\mathrm{PV} \gamma=$ constant
Differentiating
$\frac{\mathrm{dP}}{\mathrm{dV}}=-\frac{\gamma \mathrm{P}}{\mathrm{V}}$
$\frac{\mathrm{dP}}{\mathrm{P}}=-\frac{\gamma \mathrm{dV}}{\mathrm{V}}$