Question

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, 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).

Answer 1

Given,

Radius of the balloon, r = 10 m

∴ Volume of the balloon  = `4/3pi"r"^3`

`= 4/3 xx22/7 xx 10^3`

`= 4190.5 " m"^3 ("approx")`

Thus, the volume of the displaced air is 4190.5 m³.

Given,

Density of air = 1.2 kg m^–3

Then, mass of displaced air = 4190.5 × 1.2 kg

= 5028.6 kg

Now, mass of helium (m) inside the balloon is given by,

`"m" = ("MpV")/("RT")`

Here

`"M" = 4 xx 10^(-3) "kg mol"^(-1)`

p = 1.66  bar

V = Volume of the balloon

= `4190.5 " m"^3`

`"R" = 0.083 " bar" " dm"^3 "K"^(-1) "mol"^(-1)`

`"T" = 27^@"C" = 300 "K"`

Then `"m" = (4xx10^(-3)xx1.66xx4190.5xx10^3)/(0.083 xx300)`

= 1117.5 kg (approx)

Now, total mass of the balloon filled with helium = (100 + 1117.5) kg

= 1217.5 kg

Hence, pay load = (5028.6 – 1217.5) kg

= 3811.1 kg

Hence, the pay load of the balloon is 3811.1 kg.