A hot air balloon has a volume of 2210 m3. What is the buoyant force acting on it?

Answer 1

The answer to your question depends on the temperature that the air is heated to as well as the ambient temperature outside the balloon.

Let's make an estimate that the ambient temperature is 20° C and it's a dry day. We can calculate the density of the atmospheric air by using P = ρRT or ρ = P/(RT) where P = 101,300 Pa, R =287.03 J/Kg/K, and then T = 273.15 + 20 = 293.15 K. So ρ = (101300)/(287.03•293.15) = 1.204 kg/m³

Let's estimate the "hot air" to be 100° C meaning its density is calculated as: ρ = (101300)/(287.03•373.15) = 0.9458 kg/m³

Since F = ma or F = Vρg, then:

Buoyancy force is V(ρ_{ambient air} - ρ_{hot air})g = 2210(1.204 - 1.204)(9.81) = 5596 N

But you'll need to make your own assumptions about ambient temp, whether or not it's a dry day, how hot the air is, etc.