Law of corresponding states

The law of corresponding states is an empirical law encapsulates the finding that the equations of state for many real gases are remarkably similar when they are expressed in terms of reduced temperatures (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_r = T/T_c} ), pressures, ($p_{r}=p/p_{c}$) and volumes (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_r = V/V_c} ). This law was first described by Johannes Diderik van der Waals in his 1873 thesis, and forms the subject of a paper by him in 1913 (Ref. 1).

For argon, krypton, nitrogen, oxygen, carbon dioxide and methane one has (Ref. 4)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{p_cV_c}{RT_c}\approx 0.292}

(for pressure measured in atmospheres, and volume in cm³mole^-1)

For neon, argon, and oxygen one has (Ref. 4)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{T_B}{T_c} \approx 2.7}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_B} is the Boyle temperature.

For neon, argon, krypton,and xenon one has (Ref. 4)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{T_{tp}}{T_c} \approx 0.555}

where is the triple point.

References

1. Johannes Diderik van der Waals "The law of corresponding states for different substances", Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen 15 II pp. 971-981 (1913)
2. J. de Boer and A. Michels "Contribution to the quantum-mechanical theory of the equation of state and the law of corresponding states. Determination of the law of force of helium", Physica 5 pp. 945-957 (1938)
3. Kenneth S. Pitzer "Corresponding States for Perfect Liquids", Journal of Chemical Physics 7 pp. 583-590 (1939)
4. E. A. Guggenheim "The Principle of Corresponding States", Journal of Chemical Physics 13 pp. 253-261 (1945)