Question

A gas is filled in a container of volume $V$ at ${121}^{o}C$. To what temperature should it be heated in order that $\frac{1}{4}th$ of the gas may escape out of the vessel ?

Answer 1

REF.Image

Let us take,

at ${121}^{\circ }C$ there is 'n'

mole of gas in the

container of volume 'v'

and pressure is 'p'

'v', 'n', 'p'

$T={121}^{\circ }C$

$=394k$

Now,

on heating, since the gas

escapes. Therefore the pressure will

remain constant

Applying ideal gas equation

pV= nRT

$\Rightarrow pV=nR394$ ___ (i)

Let us say, at temperature $T_0$, the no. of

moles of gas in container becomes $\frac{n}{4}$

$\Rightarrow pV=\frac{n}{4}R{T}_0$ ___ (ii)

from (i) & (ii)

$394nR=\frac{n}{4}R{T}_0$

$\Rightarrow T_0=394\times 4=1376K$

$\Rightarrow T_0=1376K$ or ${1103}^{\circ }C$