Assuming that the densities of the gases are:
density of air, ρ1 = 1.29 kg / m^3
density of helium, ρ2 = 0.179 kg / m^3
Since buoyant force and weight are two forces that are in opposite direction (buoyant force is up while weight is down), therefore equate the two:
buoyant force = weight
m g = (800 + m1) g
where m is the mass of buoyancy, g is gravity and m1 is the maximum mass of the cargo
m = 800 + m1
We know that mass is also expressed as:
m = ρ V
where ρ is density of gas and V is volume of the sphere
Since there are two interacting gases here, therefore m is:
m = (ρ1 – ρ2) V
Therefore:
(ρ1 – ρ2) V = 800 + m1
(1.29 – 0.179) (4π/3) (8.35m)^3 = 800 + m1
2709.33 = 800 + m1
m1 = 1,909.33 kg
