Question

The volume of air increases by 5% in its adiabatic expansion. The percentage decrease in its pressure will be-

• A. 5%
• B. 6%
• C. 7%
• D. 8%

Answer 1

The correct option is C 7%

In an adibatic expansion,

$P{V}^{\gamma }=constant$

Differentiating the above equation,

$dP.V^{\gamma }+\gamma V^{\gamma -1}.PdV=0$

$\Rightarrow \frac{dP}{P}=-\gamma \frac{dV}{V}$

Air is primarily a diatomic gas, so

$\Rightarrow \frac{dP}{P}=-\left(1.4\right)\times 5=-7$ %

$\gamma =1.4$