A balloon containing 1 mole air at 1 atm initially is filled further with air till pressure increases to 4 atm. The intial diameter of the ballon is 1 m and the pressure at each stage is proportional to diameter of the balloon. How many moles of air added to change the pressure from 1 atm to 4 atm.

257

255

256

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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 intial diameter of the ballon is 1 m and the pressure at each stage is proportional to diameter of the balloon. How many moles of air added to change the pressure from 1 atm to 4 atm.

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Answer: cSolution: (c)

P \propto d, p = k d and k = \frac{1 atm}{1 metre}

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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Question Text	A balloon containing 1 mole air at 1 atm initially is filled further with air till pressure increases to 4 atm. The intial diameter of the ballon is 1 m and the pressure at each stage is proportional to diameter of the balloon. How many moles of air added to change the pressure from 1 atm to 4 atm.
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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 intial diameter of the ballon is 1 m and the pressure at each stage is proportional to diameter of the balloon. How many moles of air added to change the pressure from 1 atm to 4 atm.

Text solutionVerified

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