Ideal-gas equation of state

Kinetic theory explains macroscopic thermal quantities through the motion of enormous numbers of molecules. During the nineteenth century, physicists including Rudolf Clausius and James Prescott Joule developed links among heat, work, and microscopic motion, establishing the modern picture of an ideal gas. If molecules collide elastically and interactions between collisions can be neglected, pressure is related to momentum transfer at the container walls, while temperature reflects the average translational kinetic energy. The equation of state pV = nRT combines pressure p, volume V, amount of substance n, and absolute temperature T in an equilibrium relation. Holding other variables fixed shows that p rises with T or n and falls as V grows; on a p–V plot, each fixed temperature gives an isotherm. Real gases approximate this model only under suitable conditions, especially when density is not too high and intermolecular interactions are weak. The animation and graph illustrate trends but do not represent every collision, molecular size, or deviation of a real gas.