A balloon containing 1 mole air at $1 a t m$ initially is filled further with air till pressure increases to $4 a t m$ . The initial diameter of the balloon is $1 m$ and the pressure at each stage is proportion to diameter of the balloon. How many number of moles of air is added to change the pressure from $1 a t m$ to $4 a t m$ ?

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Solution

As we know,
$P \propto d; P = k d$ and $k = \frac{1 a t m}{1 m e t r e}$
$P V = n R T; k d (\frac{1}{6} π d^{3}) = n R T$ ;
$\frac{d_{1}^{4}}{d_{2}^{4}} = \frac{n_{1}}{n_{2}}; \frac{1}{4^{4}} = n_{1} / n_{2}; n_{2} = 256$
no.of moles added $= 256 - 1 = 255$

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As we know,P∝d;P=kd and k=1atm1metrePV=nRT;kd(16πd3)=nRT;d41d42=n1n2;144=n1/n2;n2=256no.of moles added=256−1=255

As we know,
$P \propto d; P = k d$ and $k = \frac{1 a t m}{1 m e t r e}$
$P V = n R T; k d (\frac{1}{6} π d^{3}) = n R T$ ;
$\frac{d_{1}^{4}}{d_{2}^{4}} = \frac{n_{1}}{n_{2}}; \frac{1}{4^{4}} = n_{1} / n_{2}; n_{2} = 256$
no.of moles added $= 256 - 1 = 255$