Question

For an adiabatic expansion of perfect gas $\frac{\Delta P}{P}$ is equal to:

• A. $\frac{\Delta V}{V}$
• B. $\gamma \frac{\Delta V}{V}$
• C. $-\gamma \frac{\Delta V}{V}$
• D. $-{\gamma }^2\frac{\Delta V}{V}$

Answer 1

The correct option is C $-\gamma \frac{\Delta V}{V}$

$P{V}^{\gamma }$=constant (for adiabatic process)
$P\gamma V^{\gamma -1}dV+V^{\gamma }.dP=0\Rightarrow P\gamma \frac{dV}{V}+dP=0\Rightarrow \gamma \frac{dV}{V}+\frac{dP}{P}=0\Rightarrow \frac{dP}{P}=-\gamma \frac{dV}{V}$