Equation of state: Any equation that relates the pressure, temperature, and specific volume of a substance.
The simplest and best-known equation of state for substances in the gas phase is the ideal-gas equation of state. This equation predicts the P-v-T behavior of a gas quite accurately within some properly selected region.

Ideal gas equation of state

R: gas constant

M: molar mass (kg/kmol)

R_u: universal gas constant

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Mass = Molar mass $\times$ Mole number

Ideal gas equation at two states for a fixed mass

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Various expressions of ideal gas equation

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Real gases behave as an ideal gas at low densities (i.e., low pressure, high temperature).

Figure 3-43 Properties per unit mole are denoted with a bar on the top.

Is Water Vapor an Ideal Gas?

At pressures below 10 kPa, water vapor can be treated as an ideal gas, regardless of its temperature, with negligible error (less than 0.1 percent).
At higher pressures, however, the ideal gas assumption yields unacceptable errors, particularly in the vicinity of the critical point and the saturated vapor line.
In air-conditioning applications, the water vapor in the air can be treated as an ideal gas. Why?
In steam power plant applications, however, the pressures involved are usually very high; therefore, ideal-gas relations should not be used.

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