# Dieterici equation of state

The **Dieterici** equation of state ^{[1]} is given by

where (Eq. 8 in ^{[2]}):

and

where is the pressure, is the temperature and is the molar gas constant. is the critical temperature and is the pressure at the critical point.

## Sadus modification

Sadus ^{[3]} proposed replacing the repulsive section of the Dieterici equation with the Carnahan-Starling equation of state, which is often used to describe the equation of state of the hard sphere model, resulting in (Eq. 5):

where is the packing fraction.

This equation gives:

and

## References

- ↑ C. Dieterici, Ann. Phys. Chem. Wiedemanns Ann. 69, 685 (1899)
- ↑ K. K. Shah and G. Thodos "A Comparison of Equations of State", Industrial & Engineering Chemistry
**57**pp. 30-37 (1965) - ↑ Richard J. Sadus "Equations of state for fluids: The Dieterici approach revisited", Journal of Chemical Physics
**115**pp. 1460-1462 (2001)