Question

A balloon containing $1$ mole air at $1$ atm initially is filled further with air till pressure increases to $3$ atm. The initial diameter of the balloon is $1$ m and the pressure at each state is proportion to diameter of the balloon. Calculate number of moles of air added to change the pressure from $1$ atm to $3$ atm.

Answer 1

$p\propto d;p=Kd$

$K=\frac{1atm}{1metre}$

$PV=nRT\Rightarrow Kd\left(\frac{1}{b}\Pi d^3\right)=nRT$

$K{d}^4\frac{1}{6}\Pi =nRT$

$\Rightarrow \frac{d_1^4}{d_2^4}=\frac{n_1}{n_2}\Rightarrow \frac{1}{3^4}=\frac{n_1}{n_2}\Rightarrow n_2=81$

Number of moles added= $81-1=80$