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In analytical chemistry, the Charlot equation, which can be used to find the pH of buffer solutions, can be solved using a cubic equation. In thermodynamics , equations of state (which relate pressure, volume, and temperature of a substances), e.g. the Van der Waals equation of state , are cubic in the volume.
Proposed in 1873, the van der Waals equation of state was one of the first to perform markedly better than the ideal gas law. In this equation, usually is called the attraction parameter and the repulsion parameter (or the effective molecular volume). While the equation is definitely superior to the ideal gas law and does predict the formation ...
Casus irreducibilis (from Latin 'the irreducible case') is the name given by mathematicians of the 16th century to cubic equations that cannot be solved in terms of real radicals, that is to those equations such that the computation of the solutions cannot be reduced to the computation of square and cube roots.
The nested radicals in this solution cannot in general be simplified unless the cubic equation has at least one rational solution. Indeed, if the cubic has three irrational but real solutions, we have the casus irreducibilis, in which all three real solutions are written in terms of cube roots of complex numbers. On the other hand, consider the ...
Moreover, analytic solutions to cubic functions have been known for centuries and are even faster for computers. The Redlich-Kwong equation of state may also be expressed as a cubic function of the molar volume. [7] For all Redlich–Kwong gases: = where: Z c is the compressibility factor at the critical point
Cubic equations of state originated from the van der Waals equation of state. Hence, all cubic equations of state can be considered 'modified van der Waals equation of state'. There is a very large number of such cubic equations of state. For process engineering, cubic equations of state are today still highly relevant, e.g. the Peng Robinson ...
The cubic equation of state (EOS) are very popular equations that are sufficiently accurate for most industrial computations both in vapor-liquid equilibrium and molar volume. Their weakest points are perhaps molar volum in the liquid region and in the critical region.
A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition, subtraction, multiplication, division, raising to integer powers, and extraction of n th roots (square roots, cube roots, etc.). A well-known example is the quadratic formula