Question

A gas is filled in a vessel at ${27}^{\circ }C$. To what temperature should it be heated in order that $\frac{1}{3}rd$ of the gas may escape out of the vessel?

Answer 1

Initial temperature is given as,

$T_1=27+273$

$=300K$

If initially the numbers of molecules are $n$ and after escape out the left molecules will be $\frac{2}{3}n$.

Since, the pressure is constant and the temperature is inversely proportional to the numbers of molecules.

It can be written as,

$\frac{T_1}{T_2}=\frac{n_2}{n_1}$

$\frac{300}{T_2}=\frac{\frac{2}{3}n}{n}$

$T_2=450K$

$=177{}^{\circ }C$

Thus, the heating temperature is $177{}^{\circ }C$.