Question

Keeping the temperature fixed, nitrogen is compressed four times of its initial pressure. The volume of gas in the container changes from $20\text{cc}$ to ${\text{V}}_2\text{cc}$. Find the final volume ${\text{V}}_2$.

• A. $5\text{cc}$
• B. $10\text{cc}$
• C. $80\text{cc}$
• D. $40\text{cc}$

Answer 1

The correct option is A $5\text{cc}$

When the temperature of a gas is kept constant, the volume $\left(\text{V}\right)$ of a fixed mass of gas is inversely proportional to its pressure $\left(\text{P}\right)$.

$\text{P}\propto \frac{1}{\text{V}}⟹{\text{P}}_1{\text{V}}_1={\text{P}}_2{\text{V}}_2$

The final volume, ${\text{V}}_2=\frac{{\text{P}}_1}{{\text{P}}_2}{\text{V}}_1$
Given: the gas is compressed four times, i.e. the final pressure ${\text{P}}_2$ is four times the initial pressure ${\text{P}}_1$.
Also ${\text{V}}_1=20\text{cc}$

${\text{V}}_2=\frac{{\text{P}}_1}{{\text{P}}_2}{\text{V}}_1$

$⟹\frac{1}{4}\times 20=5\text{cc}$