Any thermodynamic property,

, can be expressed as the sum of an ideal gas contribution and a residual non-ideal contribution:

, where

and

are the ideal gas and residual contributions, respectively. For a given equation of state, the residual contribution can then be expressed as a function of

,

, and compressibility factor

. In this Demonstration, the compressibility factor for a single gas chemical species (acetylene) is computed, from which the enthalpy (

in

) and entropy (

in

can be determined for given

and

. You can select from one of three cubic equations of state (Redlich–Kwong, Soave–Redlich–Kwong, or Peng–Robinson) as well as the temperature (in

) and the pressure (in

). The reference state is taken an ideal gas at

and

. This information is then used to obtain the molar volume (in

) as well as additional thermodynamics properties such as the Gibbs free energy (

in

), Helmholtz free energy (

in

), and internal energy (

in

). In addition,

is plotted versus reduced pressure

for a user-specified reduced temperature (

), where

and

are the critical pressure and temperature for acetylene. For an ideal gas

.