Question

A gas is filled in a cylinder, its temperature is increased by $20\%$ on kelvin scale and volume is reduced by $10\%$. How much percentage of the gas will leak out:

• A. $40\%$
• B. $30\%$
• C. $15\%$
• D. $25\%$

Answer 1

The correct option is B $30\%$

$PV=nRT$ $[n\to$ Np.of moles $]$

$log\left(PV\right)=log\left(nRT\right)$

$logP+logV=logn+logRt$

Differentiate it

$\frac{△P}{P}+\frac{△V}{V}=\frac{△n}{n}+\frac{△T}{T}$

$\because$ It is filled in a rigid cylinder

$△P=0$

$\frac{△V}{V}\times 100=-10$

$\frac{△T}{T}\times 100=20$

$\therefore -10=\frac{△n}{n}\times 100+20$

$\frac{△n}{n}\times 100=-30$

$\because n=\frac{m}{M}$

Where $m\to$ Mass of gas leaked

$M\to$ Molar mass

$\therefore \frac{△m}{m}\times 100=-30$

$\therefore 30\%$ gas will leak out