Question

In an adiabatic process, the pressure is increased by $\frac{2}{3}$%. If $\gamma =\frac{3}{2}$, then the volume decreases by nearly

• A. $\frac{4}{9}$%
• B. $\frac{2}{3}$%
• C. $1\%$
• D. $\frac{9}{4}$%

Answer 1

Answer: (A)

$\frac{4}{9}$%

$P{V}^{3/2}$ = K
$\log P+\frac{3}{2}\log V=\log K$

$\frac{\Delta P}{P}+\frac{3}{2}\frac{\Delta V}{V}$ = 0
$\frac{\Delta V}{V}=-\frac{2}{3}\frac{\Delta P}{P}$
or $\frac{\Delta V}{V}=-\frac{2}{3}\times \frac{2}{3}$
$=-\frac{4}{9}$