Question

For an adiabatic expansion of a perfect gas,the value of $\frac{\Delta P}{P}$ is equal to

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

Answer 1

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

For adiabatic process: $P{V}^{\gamma }=$constant

Taking derivative $dP{V}^{\gamma }+\gamma P{V}^{\gamma -1}dV=0$

$dP{V}^{\gamma }=-\gamma P{V}^{\gamma -1}dV$

$\frac{dP}{P}=-\gamma \frac{V^{\gamma -1}}{V^{\gamma }}dV\frac{\Delta P}{P}=-\gamma \frac{\Delta V}{V}$