Question

The pressure exerted by $12g$ of an ideal gas at temperature $t^{\circ }C$ in a vessel of $V$ litre is one atmosphere. When the temperature is increased by ${10}^{\circ }C$ at the same volume, the pressure increases by $10\%$. Calculate the temperature $t$ and volume $V$.

(Molecular mass of the gas $=120$).

Answer 1

As the volume is constant, pressure law can be applied, that is :

$\frac{P_1}{P_2}=\frac{T_1}{T_2}$

$\frac{1}{1.1}=\frac{t+273}{t+283}$

$t=-{173}^{\circ }C=100K$

Now, applying gas equation,

$PV=nRT$

or $V=\frac{n}{P}RT=\frac{12\times 0.082\times 100}{120\times 1}=0.82litre$