A balloon of diameter $20 m$ weighs $100 K g$ . Calculate its payload if it is filled with helium at $1.0 a t m$ and $27^{\circ} C$ . Density of air is $1.2 K g m^{- 3} (R = 0.082 d m^{3} atm K^{- 1} m o l e^{- 1})$

$4260 K g$

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$4395 K g$

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$4247 K g$

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$4463 K g$

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Solution

The correct option is C
$4247 K g$

Volume of balloon = $\frac{4}{3} π r^{3} = \frac{4}{3} \times \frac{22}{7} \times 10^{3} = 4190.47 m^{3}$
Mass of the air displaced = 4190.47 $\times$ 1.2 = $5028.56 K g$
No of moles of helium in the balloon=(PV/RT)
$= \frac{1 \times 4190.47 \times 10^{3}}{0.082 \times 300}$
=170344
Mass of helium = $4 \times 170.344 \times 10^{3}$ = $681.376 K g$
Mass of filled balloon = 681.376+100 = $781.376 K g$
Pay load = Mass of air displaced - Mass of filled balloon
=5028.56-781.376
= $4247.184 K g$

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A balloon of diameter $20 m$ weighs $100 K g$ . Calculate its payload if it is filled with helium at $1.0 a t m$ and $27^{\circ} C$ . Density of air is $1.2 K g m^{- 3} (R = 0.082 d m^{3} atm K^{- 1} m o l e^{- 1})$

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