Ideal gas pressure to net force

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Homework Help Overview

The discussion revolves around a hot air balloon scenario, focusing on the relationship between the ideal gas properties and the net force acting on the balloon. Participants are exploring how the pressure, volume, and temperature of the air inside the balloon relate to the buoyant force that lifts it, while neglecting the weight of the balloon itself.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the ideal gas law and the relationship between pressure, volume, and temperature. There is uncertainty about how to account for the external air volume and how it affects the net force. Questions are raised regarding the implications of temperature changes on pressure and volume, and whether the net force refers to the buoyant force.

Discussion Status

Some participants have provided insights into the behavior of gases under changing temperatures and the implications for buoyancy. There is an ongoing exploration of how the properties of the gas change and how this relates to the net force on the balloon. Multiple interpretations of the problem are being considered, particularly regarding the effects of temperature and the open nature of the balloon.

Contextual Notes

Participants note the lack of information regarding the volume of the air outside the balloon, which complicates the calculations. The discussion also touches on the assumption that the weight of the balloon itself is negligible, which may influence the analysis of forces involved.

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

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