The equation of state is an equation that relates physical quantities, such as pressure, volume, temperature, and the number of moles, of a thermodynamics system with each other. The equation relating physical quantities with each other can be a simple mathematical expression or too complicated to express in mathematical form. In either case, a relationship between physical quantities exists. If the equation of state cannot be expressed in a mathematical form, then experimental data and numerical tables are used to study the relationship between different physical quantities.
Consider a gas cylinder having initial pressure and volume at room temperature. Now, if this gas cylinder is heated to a higher temperature, the pressure exerted by the gas molecule on the walls of the container increases. At a high enough temperature, the gas cylinder explodes. Here the change in temperature of the gas changes the pressure exerted by the gas molecules on the walls of the container. Any change in one of the physical quantities changes the other physical quantities, which defines the equation of state. The equation of state uses macroscopic properties to represent the state/condition of the matter in which it exists.
