The Meaning of the Term "Equation of State" in Thermodynamics
The expansion of a gas is much more complicated than the expansion of a solid or a liquid. This is because gases are able to expand to fill whatever container you put them in.
The volume of a gas depends on pressure. However, it also depends on the temperature. As if that is not enough, we also need to consider its mass. Therefore, in order to develop a proper mathematical model of a gas, we need to consider its volume, pressure, temperature, and mass. We need an equation of state.
A relation between the physical terms pressure P, volume V, and temperature T is called an equation of state. State simply means the physical condition of the system. Here, we are using parameters to specify the physical relations we are interested in. The parameters P, V, and T are called state variables.
The physical state of our gas system can change. On a very hot day you may be reluctant to turn on the oven inside your kitchen, especially if you have no air conditioning. The heat from the oven makes the temperature of the air inside the kitchen increase, and this may make it unbearably hot inside your entire efficiency apartment. Turn the oven off, and the temperature will stop increasing. When the state or physical condition of our system changes, and values such as the pressure and temperature to stop increasing or decreasing, we have reached an equilibrium state. Our observed parameters will be the same throughout the system, and on the whole will not change in time.