Can someone explain to me the concepts behind Hot Air Balloons?

[September24]

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I've been studying MCAT for a while and I still can't connect concepts of bouyancy and density to hot airballoons.


I know that to rise...the density of air inside the hot airballoon must be less than density of air outside.

1. What are different ways to reduce and increase density?

Volume stays constant usually right? Since volume is just the volume of balloon which is how much air is displaced? We can decrease pressure to decrease moles of air inside balloon or increase temperature at constant pressure to decrease (pv=nrt) moles which both decrease density of air inside balloon. This helps balloons float?

Overall, the idea behind balloons confuses me and I loose track of how changes can be made to balloons and how these changes affect bouyancy.

 

[Czarcasm]

Using the Ideal Gas equation, you can establish relationships between different variables and the density of the gas.
Re-arranging for density, you get: P/RT = n/V ==> P x MW / RT = density (grams/volume).

As you mentioned, for anything to rise, it must be less dense than its surroundings. Based on the relationships in this expression, you can determine how variables can be changed to accomplish this. MW for a given gas is constant, as is the gas constant R. Therefore, the only three variables left to consider are Pressure, Temperature, and Volume.

Consider PV=nRT once again.

There is a direct relationship between temperature and volume. Increasing temperature causes the volume to increase proportionally. Likewise, an increase in temperature increases pressure (the frequency at which molecules collide with the container) -- assuming the volume of the container is fixed (constant). But in hot air balloons this is not the case. The volume of the balloon is constantly changing to rise or fall.

Consider again the equation we derived earlier for density of the gas: P x MW / RT = density = (grams/volume). Increasing the temperature increases the volume, which in turn decreases the density of the gas. When you turn off the flame, the gas cools down causing the volume to decrease (density to increase), and the balloon begins to fall.

Hope this all makes sense.

 

[DrknoSDN]

That question sounds like it would help to think about it conceptually instead of using equations.

If you increase the temperature of a gas the average kinetic energy of all the molecules increases.
And if the kinetic energy is increased but the pressure is a constant ( 1 atmosphere) then the higher KE causes the average distance between molecules to increase.

If the gas molecules are more spread out, the density is less.

The equations work also but because hot air balloons are not "ideal" in that you cannot control for constant pressure or volume, its probably easier to think about the concept. Heating the "real" balloon causes it's volume to slightly increase as temperature increases making the math harder to visualize.