Question

By what percentage should the pressure of a given mass of gas be increased, so as to decrease its volume by $10$% at a constant temperature?

• A. $11.1$%
• B. $10.1$%
• C. $9.1$%
• D. $8.1$%

Answer 1

The correct option is A $11.1$%

We have from the Ideal Gas Equation: $PV$ = $nRT$

Since It is taken into consideration that the mass as well as the Temperature is constant.

It can be written as $PV$ = $k\left(Someconstant\right)$

Given chnage in volume = $10$ %

New volume $=V-0.1V$

$=0.9V$

The pressure for the corresponding volume $P_1$ is

$P_1\times 0.9V=k$

$P_1$ $=\frac{k}{0.9V}$

Change in pressure $=P_1-P$

$=\frac{k}{9V}$

The percentage change is $=\frac{k/9V}{k/V}\times 100$$=\frac{100}{9}$ = $11.1$ %