A balloon of dia 20m weighs 100 kg.Calculate its pay wad if it is field with helium at 1 atm and $27^{\circ} C$ . Density of air is 1.2 kg/ $m^{3}$ (4274.18 kg)

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Solution

Weight of balloon $= 100 K g$ or $10^{5} g m .$
Volume of Balloon $= \frac{4}{3} π r^{3} = \frac{4}{3} π (\frac{20}{2} \times 100)^{3} = 4 a 90 \times 10^{3} l i t$
Weight of gas $(H e)$ in balloon $= \frac{P V_{m}}{R T}$
Since, $P V = \frac{w}{m} R T)$ $= \frac{1 \times 4190 \times 10^{3} \times 4}{0.082 \times 300} = 68.17 \times 10^{4} g$
Total weight of gas and balloon $= 68.13 \times 10^{4} + 10 \times 10^{4} = 78.13 \times 10^{4}$
Weight of air displaced $= \frac{1.2 \times 4190 \times 10^{6}}{10^{3}} = 502.8 \times 10^{4} g$
Pay load $=$ weight of air displaced $-$ (weight of balloon + weight of gas)
$= 502.8 \times 10^{4} - 78.13 \times 10^{4} = 424.67 \times 10^{4} g$

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A balloon of dia 20m weighs 100 kg.Calculate its pay wad if it is field with helium at 1 atm and 27∘C. Density of air is 1.2 kg/m3 (4274.18 kg)

A balloon of dia 20m weighs 100 kg.Calculate its pay wad if it is field with helium at 1 atm and $27^{\circ} C$ . Density of air is 1.2 kg/ $m^{3}$ (4274.18 kg)