19.1:
Equation of State
For any thermodynamic system, the state of matter is described by the physical variables pressure, volume, temperature, and total mass of the matter or number of moles.
These physical variables are called state variables, and an equation that relates these physical variables with each other is termed the equation of state.
For example, consider a kettle filled with water. The state of the water inside the kettle is defined by the initial volume, pressure, and temperature. If the water is heated, the volume occupied by the water increases with temperature.
The heated water, converted to steam, occupies a larger volume at the top of the kettle and exerts high pressure on the water. This excess pressure is released when steam leaks out of the spout.
The steam, the gaseous water, is described by new values of these state variables.
The state of matter can be changed by changing one of the state variables, which causes a change in the other state variables.
19.1:
Equation of State
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.
Suggested Reading
- Young, H.D and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson; section 18.1; page 591.
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from https://openstax.org/details/books/university-physics-volume-2; section 2.1; page 68-70.