Question

A cylinder contains $10kg$ of gas at pressure of ${10}^{7}N/m^2$ . The quantity of gas taken out of the cylinder if final pressure is $2.5\times {10}^{6}N/m^2$ , is:

• A. 7.5kg
• B. 15.2kg
• C. 10.5kg
• D. none of these

Answer 1

Answer: (A)

From kinetic theory of gases $PV=\frac{1}{3}m{c}^2$
where $P$ is pressure,
$V$ is volume,
$m$ is mass and
$c$ is velocity.
$\therefore \frac{P_1}{P_2}=\frac{m_1}{m_2}$
$\Rightarrow m_2=\frac{P_2}{P_1}{m}_1$
Given, $P_1=10^{7}N/m^2$,
$P_2=2.5\times 10^{6}N/m^2$,
$m_1=10kg$ .
$\therefore m_2=\frac{2.5\times 10^6}{10^7}\times 10=2.5kg$
Quantity of gas taken out $=10-2.5=7.5kg$.