Introduction: If you've ever gone on a ride in hot air balloon (or, if you've seen a hot air balloon in a movie), you know that as the gas in the hot air balloon is heated using fire on top of the balloon, the increase in the amount of heat in the hot air balloon will increase the volume of the hot air balloon. As a result, the hot balloon expands and is able to float. This is one of many examples of applications of what is known as the ideal gas equation: `PV=nRT`, where P=pressure, V=volume, n=number of moles, R=gas constant, and T=temperature

The ideal gas equation can be applied to calculate the pressure, volume, number of moles, or temperature of a gas at certain conditions, provided that all of the other values are given. Generally, for a given temperature and number of moles, an increase in pressure will lead to a decrease in temperature, since the product of pressure and temperature must remain constant, in this case. In the case of the hot air balloon, assuming that the pressure and the number of moles remain the same, the volume must increase in order to match the increase in the temperature. Though seemingly simple, the ideal gas allows for a rich exploration of the behavior of gases as a whole.