What is the principle of hot-air ballooning, in terms of the particle model of matter?

Air is a gas formed of atoms and simple molecules (i.e. diatomic oxygen and nitrogen). As you heat the air the kinetic energy of the atoms and molecules increase so also does the average spacing between them. Accordingly, the density of the hot air is lower than the surrounding, colder air and it rises up into the balloon fabric. This lifts the balloon.

Jim is basically right. The principle is buoyancy per Archimedes. For a non-particle model, gases behave according to Boyles Law: PV=nRT. How that relates to the particle model of matter is more complex. Air varies in composition but it is approximately 78% N2 + 20% O2 + small amounts of H2O, CO2, CO, Ar, and other gases. It is certainly appropriate to consider these gas molecules as particles. Temperature is a measure of the average kinetic energy of particles. Related to particle model of matter, one characteristic of gases at a particular temperature is the mean free path, how far the average particle travels in a straight line before it bumps into another particle. This is related to pressure and density. In air at standard T & P, the mean free path is pretty short, tiny tiny fractions of a mm, not an awful lot bigger than the average diameter of the particles.

Sounds like an interesting assignment. Hope this helps

These hot air balloons fly because of two fundamental principles of physics: the ideal gas law and Archimedes's principle.

Ideal Gas Law

The ideal gas law is a mathematical relationship between the volume pressure and temperature of a gas. For a given quantity of gas, the pressure, P, multiplied by the volume, V, divided by the temperature, T, remains a constant.

If a gas is heated, as in a hot air balloon, then its volume will increase. A heater in the balloon's basket heats the air inside the balloon and blows hot air into the balloon. As the volume of gas increases, it fills the balloon. Soon the balloon is full of hot air. If the air continues to heat up, it expands and flows out of the hole in the bottom of the balloon.

Hence a balloon filled with hot air contains fewer air molecules than the same balloon inflated to the same size with cool air. A hot air balloon will therefore be less dense than a balloon filled with cool air as a consequence of the ideal gas law.

Archimedes's Principle

Archimedes's principle states that when an object is suspended in a fluid, the buoyant force acting on an object is equal to the weight of the fluid displaced. As a consequence of Archimedes's principle, an object will float in a fluid if it is less dense than the fluid.

Ordinarily people think of a fluid as being a liquid, however in science a fluid is defined as either a liquid or a gas. Air is therefore a fluid and Archimedes's principle applies to floating in air as well as floating in a liquid.

The balloon filled with hot air is less dense than when it is filled with cool air. For the balloon to rise and lift the basket and passengers off the ground, the hot air in the balloon must have a low density. The balloon, basket, and passengers combination must weigh less than the total amount of air displaced by the balloon. Then the upward buoyant force exceeds the downward weight (gravitational force).

Helium filled balloons float by the same principle because helium gas is much less dense than air.

The hot air filling the balloon reduces its density according to the ideal gas law. When its total density is less than the density of air, it floats according to Archimedes's principle.

The density difference is greater when the air temperature is cooler, so hot air balloons are often inflated in the cooler predawn hours.

Read more at Suite101: Why do Hot Air Balloons Fly: How the Ideal Gas Law and Archimedes's Principle Apply to Ballooning http://physics.suite101.com/article.cfm/why_do_hot...

warm air balloons are consistent with an extremely easy medical concept: warmer air rises in cooler air. in reality, warm air is lighter than cool air, with the aid of fact it has much less mass according to unit of quantity.

warm air balloons are in line with an incredibly uncomplicated scientific concept: warmer air rises in cooler air. in fact, warm air is lighter than cool air, because of the fact it has much less mass in line with unit of quantity.

I wish to ask the same question as the previous person.