Question

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to

• A. $-\gamma \frac{V}{dV}$
• B. $-\frac{dV}{\gamma V}$
• C. $\frac{dV}{V}$
• D. $-\gamma \frac{dV}{V}$

Answer 1

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

Equation of state of an adiabatic process is given by
$P{V}^{\gamma }$ = constant
Differentiating on both sides, we get
$V^{\gamma }dP+\gamma P{V}^{\gamma -1}dV=0$
or $\frac{dP}{P}=-\gamma \frac{dV}{V}$
Thus, option (d) is the correct answer.