Question

The relation between pressure $p$ and volume $v$ is given by $p{v}^{\frac{1}{4}}$ = Constant. If the percentage decrease in volume is $\frac{1}{2}$, then the percentage increase in pressure is

• A. $-\frac{1}{8}$
• B. $\frac{1}{16}$
• C. $\frac{1}{8}$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$\frac{1}{8}$

$p{v}^{\frac{1}{4}}=c$ (constant )

$\Rightarrow p=c{v}^{-\frac{1}{4}}$

$\Rightarrow \log p=\log c-\frac{1}{4}\log v$, take log both sides

$\Rightarrow \frac{\Delta p}{p}=-\frac{1}{4}\frac{\Delta v}{v}=-\frac{1}{4}\cdot (-\frac{1}{2})=\frac{1}{8}$