Why Does Air Expand With Heat?

Kinetic Energy and Heat

• The kinetic energy of an air molecule equals its translational (forward-velocity) kinetic energy plus its rotational energy plus its vibrational energy. To simplify the argument, let's focus on just monatomic gas molecules, so that we only have to think about translational kinetic energy, which equals one-half the atom's mass times the square of its velocity. The faster the air atoms go, the more energy they have with which to do work and push against their surroundings. Thus, greater kinetic energy means more temperature, which results in more pressure felt by the surroundings containing the gas.
  
  

Expansion and Cooling

• Just as heating of a gas leads to expansion against its surroundings, expansion of the gas leads to its cooling. For example, liquid carbon dioxide released from a fire extinguisher turns into a very cool gas. Why doesn't just the pressure go down? An expanding gas does work moving its surroundings out of the way. Work, which is the application of a force to make objects move over a distance, is a type of energy. By the law of conservation of energy, the energy elsewhere must go down. In the case of the extinguisher, the carbon dioxide gas loses kinetic energy. Thus, its temperature goes down.
  
  

A Distinction Between Pressure and Temperature

• If heating comes from higher kinetic energy, then why do pressure and temperature feel different? For example, touching a warm car hood feels different from catching a baseball with your bare hand. Both impart kinetic energy, but feel very different. And holding your hand out the car window into the wind actually feels cool, not warm.
  
  

Equilibrium

• To help understand this distinction, it helps to understand the difference between pressure equilibrium and temperature equilibrium. A movable piston separating two gases in a box will move until the pressures on both sides are equal. In other words, the average kinetic energies times the number of molecules per volume will be equal on both sides. But thermal equilibrium has not necessarily been reached yet.
  
  It can be shown that temperature equilibrium won't be reached until the average kinetic energy per molecule is the same between the two species (as opposed to the equality after multiplying by the density). This could require more shifting of the piston to maintain pressure equilibrium, as the gases approach equilibrium.
  
  

The Bottom Line

• The bottom line is that you can have pressure equilibrium without thermal equilibrium. Although pressure and heat are functions of kinetic energy, pressure equilibrium can be achieved by increased density, without a transfer in kinetic energy having occurred. Therefore, although an increase in kinetic energy leads to an increase in temperature and pressure, an increase in pressure need not lead to an increase in kinetic energy. It can also lead to an increase in density.