Question

By what percentage should the pressure of a given mass of a gas be increased so as to decrease its volume by $20\%$ at a constant temperature?

• A. $20\%$
• B. $25\%$
• C. $10\%$
• D. $5\%$

Answer 1

The correct option is B $25\%$

According to Boyle's law for a given mass of an ideal gas at
$PV=K$ (constant) at constant temperature

$\therefore P_1{V}_1=P_2{V}_2$
Where, $P_1$ and $V_1$ are initial pressure and volume
and $P_2$ and $V_2$ are final pressure and volume
$\Rightarrow \frac{P_2}{P_1}=\frac{V_1}{V_2}\text{As given};V_2=V_1-\frac{V_1\times 20}{100}=\frac{80}{100}{V}_1\Rightarrow V_2=\frac{4}{5}{V}_1\therefore \frac{V_1}{V_2}=\frac{5}{4}\Rightarrow \frac{P_2}{P_1}=\frac{5}{4}\Rightarrow \frac{P_2}{P_1}-1=\frac{5}{4}-1\Rightarrow \frac{P_2-P_1}{P_1}=\frac{5-4}{4}=\frac{1}{4}\Rightarrow \frac{P_2-P_1}{P_1}\times 100=\frac{1}{4}\times 100=25\%$