Question

For a reversible adiabatic ideal gas expansion $\frac{dP}{P}$ is equal to:

• A. $\gamma \frac{dV}{V}$
• B. $-\gamma \frac{dV}{V}$
• C. $\left(\frac{\gamma }{\gamma -1}\right)\frac{dV}{V}$
• D. $\frac{dV}{V}$

Answer 1

The correct option is B $-\gamma \frac{dV}{V}$

$P{V}^{\gamma }=constant,P.\gamma V^{\gamma -1}.dV+V^{\gamma }.dP=0$
$\therefore \frac{dP}{P}=-\gamma .\frac{dV}{V}$