Payload is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the payload, when a balloon of radius 10 m of mass 100 kg is filled with helium at 1.66 bar at 27 $^{\circ} C$ . (Density of air = 1.2 kg m $^{3}$ and R = 0.083 bar dm $3$ K $^{- 1}$ mol $^{- 1}$ )

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Solution

The volume of the balloon is $V = \frac{4}{3} π r^{3}$ .
The radius of balloon is 10 m.
Hence, the volume of the balloon is $V = \frac{4}{3} \times 3.1416 \times (10)^{3} = 4186.7 m^{3}$ .
The mass of displaced air is obtained from the product of volume and density. It is $4186.7 \times 1.2 = 5024.04 k g$ .

The number of moles of gas present are $n = \frac{P V}{R T}$ $= \frac{1.666 \times 4186.7 \times 10^{3}}{0.083 \times 300} = 279.11 \times 10^{3}$ .

Note: Here, the unit of volume is changed from $m^{3}$ to $d m^{3}$ .
$1 m^{3} = 1000 d m^{3}$ .

Mass of helium present is obtained by multiplying the number of moles with molar mass. It is $279.11 \times 10^{3} \times 4 = 1116.44 \times 10^{3} g = 1116.4$ kg.
The mass of filled balloon is the sum of the mass of the empty ballon and the mass of He. It is $100 + 1116.4 = 1216.4$ kg.
Pay load $=$ mass of displaced air $-$ mass of balloon $= 5024.04 - 1216.44 = 3807.6$ kg

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Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius 10 m, mass 100 kg is filled with helium at 1.66 bar at 27°C. (Density of air = 1.2 kg m^–³ and R = 0.083 bar dm³ K^–¹ mol^–¹).

Calculate the pay load when a balloon of radius 10 m, mass 100 kg is filled with helium at 1.66 bar at 27°C. (Density air=1.2 kg m^-3and R=0.083 bar dm³K^-1mol^-1)

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 $1.2 K g m^{- 3} (R = 0.082 d m^{3} atm K^{- 1} m o l e^{- 1})$

Q. A balloon of diameter

20 m

weighs

100 k g

. Calculate its paylod 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} a t m K^{- 1} m o l^{- 1})

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Payload is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the payload, when a balloon of radius 10 m of mass 100 kg is filled with helium at 1.66 bar at 27 ∘C. (Density of air = 1.2 kg m3 and R = 0.083 bar dm 3 K−1 mol−1)