# Equation of state

### 1787

However, Mariotte's work was not published until 1676. === Charles's law or Law of Charles and Gay-Lussac (1787) === In 1787 the French physicist Jacques Charles found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to roughly the same extent over the same 80-kelvin interval.

### 1873

However, later work revealed that the number should actually be closer to 273.2, and then the Celsius scale was defined with 0°C = 273.15K, giving: pV_m = R \left(T_C + 273.15\ {}^\circ\text{C}\right). === Van der Waals equation of state (1873) === In 1873, J.

The substance-specific constants a and b can be calculated from the critical properties p_c, T_c, and V_c (noting that V_c is the molar volume at the critical point) as: a = 3 p_c V_c^2 b = \frac{V_c}{3}. Also written as a = \frac{27(R T_c)^2}{64p_c} b = \frac{R T_c}{8p_c}. Proposed in 1873, the van der Waals equation of state was one of the first to perform markedly better than the ideal gas law.

### 1949

The largest and the lowest solution are the gas and liquid reduced volume. === Redlich-Kwong equation of state=== \begin{align} p &= \frac{R\,T}{V_m - b} - \frac{a}{\sqrt{T}\,V_m\left(V_m + b\right)} \\[3pt] a &\approx 0.42748\frac{R^2\,T_c^\frac{5}{2}}{p_c} \\[3pt] b &\approx 0.08664\frac{R\,T_c}{p_c} \end{align} Introduced in 1949, the Redlich-Kwong equation of state was a considerable improvement over other equations of the time.

### 1972

The original formulation from Soave is: \alpha = \left(1 + \left(0.480 + 1.574\,\omega - 0.176\,\omega^2\right) \left(1-T_r^{0.5}\right)\right)^2 for hydrogen: \alpha = 1.202 \exp\left(-0.30288\,T_r\right). We can also write it in the polynomial form, with: A = \frac{a \alpha P}{R^2 T^2} B = \frac{bP}{RT} then we have: 0 = Z^3-Z^2+Z\left(A-B-B^2\right) - AB where R is the universal gas constant and Z=PV/(RT) is the compressibility factor. In 1972 G.

### 1990

Values for a === Elliott, Suresh, Donohue equation of state === The Elliott, Suresh, and Donohue (ESD) equation of state was proposed in 1990.

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