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 proportional to the diameter of the balloon. How many no. of moles of air added to change the pressure from $1 a t m$ to $4 a t m$ ?

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257

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255

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256

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Solution

The correct option is C 255
$P \propto d; P = k d$ 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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A balloon containing 1 mole air at 1 atm initially is filled further with air till pressure increases to 4 atm. The initial diameter of the balloon is 1 m and the pressure at each stage is proportion to diameter of the ballon. How many moles of air have to be added to change the pressure from 1 atm to 4 atm

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The correct option is C 255P∝d;P=kd and k=1atm1metrePV=nRT;kd(16πd3)=nRT;d41d42=n1n2;144=n1/n2;n2=256No.of moles added=256−1=255.

The correct option is C 255
$P \propto d; P = k d$ 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 $= 256 - 1 = 255$ .