Payload is defined as the difference between the mass of the displaced

1.	Payload is defined as the difference between the mass of the 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 kgm-3 and R = 0.083 bar dm3 K-1 mol-1)
Answer» Payload of the balloon = mass of the displaced air - mass of the balloon. Radius of the balloon, r = 10 m Mass of the balloon, m = 100 kg Volume of the balloon = 4/3 πr³ = 4/3 π x (10 m)³ Therefore, Volume of the displaced air = 4188.8 m³ and mass of the displaced air = 4188.8 m³ x 1.2 kg m^-3 = 5026.6 kg Let W be the mass of helium gas filled into the balloon, then pV = (W/M)RT or, W = {pVM}/{RT} = {1.66 bar x 4188.8 x 10³ dm³ x 4 g mol^-1}/{0.083 bar dm³ K^-1 mol^-1 x 300 K} or, W = 1.117 x 10⁶ g = 1117.0 kg Total mass of the balloon filled with Helium = 1117.0 kg + 100 kg = 1217.0 kg Then, payload of the balloon = 5026.6 kg - 1217.0 kg = 3809.6 kg

Payload is defined as the difference between the mass of the 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 kgm-3 and R = 0.083 bar dm3 K-1 mol-1)

Answer»

Payload of the balloon = mass of the displaced air - mass of the balloon.

Radius of the balloon, r = 10 m

Mass of the balloon, m = 100 kg

Volume of the balloon

= 4/3 πr³

= 4/3 π x (10 m)³

Therefore, Volume of the displaced air = 4188.8 m³

and mass of the displaced air = 4188.8 m³ x 1.2 kg m^-3 = 5026.6 kg

Let W be the mass of helium gas filled into the balloon, then

pV = (W/M)RT

or, W = {pVM}/{RT}

= {1.66 bar x 4188.8 x 10³ dm³ x 4 g mol^-1}/{0.083 bar dm³ K^-1 mol^-1 x 300 K}

or, W = 1.117 x 10⁶ g

= 1117.0 kg

Total mass of the balloon filled with Helium

= 1117.0 kg + 100 kg

= 1217.0 kg

Then, payload of the balloon

= 5026.6 kg - 1217.0 kg

= 3809.6 kg