The ideal gas is a theoretical state of matter with no interaction between molecules. The ideal gas law, PV = NkT, describes the relationship between pressure, volume, and temperature. The law is an approximation, but it is useful for understanding gas behavior. The Van der Waal equation corrects some assumptions but is not significantly better. The ideal gas is assumed to be in equilibrium, and abandoning this assumption leads to statistical physics.
An ideal gas is a theoretical state of matter used by physicists in analyzing probability theory. The ideal gas consists of molecules that bounce off each other without interacting at all. There are no forces of attraction or repulsion between the molecules and no energy is lost in collisions. Ideal gases can be fully described by their volume, density and temperature.
The equation of state for an ideal gas, commonly known as the ideal gas law, is PV = NkT. In the equation, N is the number of molecules and k is Boltzmann’s constant, which is approximately 1.4 x 10-23 joules per kelvin. What is usually more important is that pressure and volume are inversely proportional and each is proportional to temperature. This means, for example, that if the pressure is doubled while keeping the temperature constant, then the volume of the gas must halve; if the volume of the gas is doubled while holding the pressure constant, the temperature must also double. In most examples, the number of molecules in the gas is assumed to be constant.
Of course, this is only an approximation. Collisions between gas molecules are not perfectly elastic, some energy is lost, and electrostatic forces between gas molecules exist. But in most everyday situations, the ideal gas law comes very close to the actual behavior of gases. While not used to perform calculations, keeping in mind the relationships between pressure, volume, and temperature can help a scientist intuitively understand the behavior of a gas.
The ideal gas law is often the first equation people learn when they study gases in an introductory physics or chemistry class. The Van der Waal equation, which includes some minor corrections to the basic assumptions of the ideal gas law, is also taught in many introductory courses. In practice, however, the correction is so small that if the ideal gas law is not accurate enough for a given application, then not even the Van der Waal equation will be good enough.
As in most thermodynamics, the ideal gas is also assumed to be in a state of equilibrium. This assumption is clearly false if pressure, volume, or temperature change; if these variables change slowly, a state called quasi-static equilibrium, the error can still be acceptably small. To give up the quasi-static equilibrium assumption is to abandon thermodynamics for the more complicated world of statistical physics.
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