Calculate Net Force on Hot-Air Balloon Using Ideal Gas Law | Homework Solution

[kop442000]

Homework Statement

A hot-air balloon has a volume of 1.5m^3 and is open at the bottom. If the air inside the balloon is at temperature of 75C, while the temperature of the air outside the balloon is 24C, at a pressure of about 1 atm, what is the net force on the balloon and its contents? (Neglect the Weight of the balloon itself).

Homework Equations

The Attempt at a Solution

I know that this question is about the ideal-gas law, but for some reason I just can't think how to do it.

 

[Kurdt]

Force is pressure times area. This is all about the pressure of the gas inside the balloon.. That should be enough to get you going.

 

[Doc Al]

Consider Archimedes' principle. How does the density of the air inside the balloon compare to that outside?

 

[kop442000]

So to find the density, I presume I first find the number of moles in the balloon using the ideal gas law. But to do so, can I assume that the pressure inside the balloon is the same as the pressure outside?

When I do this, I calculate 35 moles per m^3. This leads me to a density of just over 1kg/m^3. This is compared to the density of the air outside of 1.19kg/m^3

Oh.. ok I got it. So now I just figure out how much more gravity would pull down 1.5m^3 of the normal density air, and this is the force on the balloon.

Initially my problem was just that I wasn't sure if I could assume pressure inside to be equal to outside - because I thought the material of the balloon would add its own elasticity to the forces making the balloon smaller - but I guess because the bottom of the balloon is open this never becomes an issue.

Anyway, thanks for the help!