Equations of State

Equations that relate the pressure, temperature and specific volume or molar volume of a substance. They predict the relationship of a “gas” reasonably well within selected regions.

Boyle's law:

at constant pressure

or,

Constant at constant temperature

Charles' Law:

At constant pressure

At constant volume

Boyle's law and Charles' law can be combined to yield

Where R is the characteristic gas constant. If the specific volume is substituted by the molar volume, then R is substituted by the universal gas constant, 8.314 kJ / kmol K. Again, it can be shown that for an ideal gas .

In summary, the Ideal gas equation:

where R is the specific constant

, where is the universal gas constant (8.314 kJ / k mole K) M is the molar mass, defined as the mass of one mole of a substance. We can also write where is the molar volume.

Example: M = 28 kg / kmol for nitrogen (since its molar mass is 28)

M =32 kg / kmol for oxygen ( O₂ with a molar mass of 32)

Note: Many gases such as air, oxygen can be treated as ideal gases. However, dense gases such as water vapor and refrigerant vapor should not be treated as ideal gas. Use property table instead.