Question

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

• A. ${\gamma }^{1/2}\frac{\Delta V}{V}$
• B. $-\frac{\Delta V}{V}$
• C. $-\gamma \frac{\Delta V}{V}$
• D. ${\gamma }^2\frac{\Delta V}{V}$

Answer 1

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

Differentiate $PV=constant$ w.r.t. $V$
$\Rightarrow$$P\Delta V+V\Delta P=0$
$\Rightarrow$$\frac{\Delta P}{P}=-\frac{\Delta V}{V}$