A ballon of diameter 21 m weighs 100 kg - Calculate its payload if it is filled with helium at 1-0 atm and 27- C- Density of air is 1-2 kg m -3 R -0-08 dm 3 atm K -1 mol -1A- 4912-7 kgB- 3520-14 kg- 5250-25 kgD- 3888-12 kg

The correct option is A 4912. 7 kgVolume of the balloon = 43π r^3 = 43×227× (10.5)^3 = 4851 m^3 Mass of the air displaced = 4851 × nbsp; 1.2 = 5821.20 kg ...

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Standard XII

Chemistry

Pressure and Temperature

A ballon of d...

Question

A ballon of diameter $21 m$ 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 $1.2 {kg m}^{- 3}$
$(R = 0.08 d m^{3} {atm K}^{- 1} m o l^{- 1})$

4912. 7 k g

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3520.14 k g

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5250.25 k g

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3888.12 k g

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Solution

The correct option is A $4912. 7 k g$
Volume of the balloon $= \frac{4}{3} π r^{3} = \frac{4}{3} \times \frac{22}{7} \times (10.5)^{3} = 4851 m^{3}$
Mass of the air displaced $= 4851 \times 1.2 = 5821.20 kg$
Number of moles of helium in the balloon = $\frac{P V}{R T}$
$= \frac{1 \times 4851 \times 10^{3}}{0.08 \times 300} = 202125 m o l$
So, mass of helium = $4 \times 202125 g = 808500 g = 808.5 k g$
Mass of filled balloon = $808.5 + 100 = 908.5 k g$
Payload = Mass of air displaced - Mass of filled balloon
$= 5821.2 - 908.5 = 4912 .7 k g$

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A ballon of diameter 21 m weighs 100 kg. Calculate its payload if it is filled with helium at 1.0 atm and 27 ∘C. Density of air is 1.2 kg m−3 (R=0.08 dm3atm K−1mol−1)

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