Question

A cylinder contains $10 \,kg$ 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 $P V=\frac{1}{3} m c^{2}$
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}=10\, kg$ .
$\therefore m_{2}=\frac{2.5 \times 10^{6}}{10^{7}} \times 10=2.5 \,kg$
Quantity of gas taken out $=10-2.5=7.5\, kg$.