Ideal gas pressure to net force

[VonWeber]

So I know the volume of a hot air balloon and the temperatures of the air (ideal gas) inside the balloon and outside of it. I know the pressure of the air. And I need to find the Net force on the balloon and contents but neglecting the weight of the balloon itself. I thinkthere must be some way in the problem to use the ideal gas conditions P1*V1/T1 = P2*V2/T2 and that P=F/A to solve for a force. But since I don't have a V for the air outside I'm not sure how. I'm wondering if what's being meant by the 'net force' is the force that lifts the balloon up in which case I might have to find densities like in boyancy problems?

 

[Andrew Mason]

So I know the volume of a hot air balloon and the temperatures of the air (ideal gas) inside the balloon and outside of it. I know the pressure of the air. And I need to find the Net force on the balloon and contents but neglecting the weight of the balloon itself. I thinkthere must be some way in the problem to use the ideal gas conditions P1*V1/T1 = P2*V2/T2 and that P=F/A to solve for a force. But since I don't have a V for the air outside I'm not sure how. I'm wondering if what's being meant by the 'net force' is the force that lifts the balloon up in which case I might have to find densities like in boyancy problems?

This is a buoyancy problem.

Think of the pressure and volume of the balloon. Does either change when temperature increases? What quantity in the ideal gas equation changes when the temperature increases?

AM

 

[VonWeber]

The Pressure would change, but since the bottom of the balloon is open the number of molecules can also change.

 

[Andrew Mason]

The Pressure would change, but since the bottom of the balloon is open the number of molecules can also change.

PV=nRT so as the temperature increases, PV increases. Since the balloon is open to the atmosphere, there is no way that the pressure inside the balloon can be greater than the pressure outside. So pressure cannot increase. This means that volume must increase. But since the balloon cannot expand, the extra volume must leave the balloon. So the contained air loses mass.

Or you could look at it this way: Neither P nor V can change. Since T = PV/nR if T increases n must decrease proportionately.

As a result, the balloon is lighter than the surrounding air. Work out the buoyancy force to get the lift.

AM