Ideal gas pressure to net force

In summary, the balloon is lighter than the surrounding air and so it has a buoyancy force that causes it to rise.
  • #1
VonWeber
52
0
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?
 
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  • #2
VonWeber said:
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
 
  • #3
The Pressure would change, but since the bottom of the balloon is open the number of molecules can also change.
 
  • #4
VonWeber said:
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
 
Last edited:

Related to Ideal gas pressure to net force

1. What is an ideal gas?

An ideal gas is a theoretical gas composed of particles that have negligible volume and do not interact with each other. This means that the particles are assumed to have no size and do not exert any forces on each other.

2. How is ideal gas pressure related to net force?

According to the ideal gas law, pressure is directly proportional to the number of gas particles and the temperature of the gas, and inversely proportional to the volume of the gas. Net force, on the other hand, is the sum of all the forces acting on an object. In an ideal gas, the particles do not interact with each other, so there are no forces between them. This means that the pressure of an ideal gas is solely determined by the number of particles and their speed, which corresponds to the net force on the container walls.

3. How does temperature affect the ideal gas pressure?

The ideal gas law states that as temperature increases, the pressure of the gas also increases, assuming all other variables remain constant. This is because an increase in temperature means an increase in the average speed of the gas particles, resulting in more frequent and forceful collisions with the container walls, leading to a higher pressure.

4. What is the relationship between volume and ideal gas pressure?

The ideal gas law also states that as volume decreases, the pressure of the gas increases, assuming all other variables remain constant. This is because when the volume decreases, the same number of gas particles are now confined to a smaller space, resulting in more frequent and forceful collisions with the container walls, leading to a higher pressure.

5. How is the number of gas particles related to the ideal gas pressure?

The ideal gas law states that as the number of particles increases, the pressure of the gas also increases, assuming all other variables remain constant. This is because with more particles, there are more collisions with the container walls, resulting in a higher pressure. Conversely, if the number of particles decreases, there are fewer collisions and the pressure decreases as well.

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