# Function

In thermodynamics, a function is a mathematical expression of one thermodynamic variable as a function of one or more other thermodynamic variables or quantities.

History
In 1673, German mathematician Gottfried Leibniz introduced the term “function” to describe a quantity related to a curve, such as a curve’s slope at a specific point. 

In 1718, Swiss mathematician Johann Bernoulli, father of Hydrodynamics author Daniel Bernoulli, had defined the function as any expression made up of a variable and some constants. 

In circa 1734, the familiar notation “f(x)” was introduced through the works of both French mathematician Alexis Clairaut and Swiss mathematician Leonhard Euler.  In 1755, Euler was using f(x) to denote the function f applied to the argument x. 

The Euler-definition of the function is said to have remained unchanged until French physicist Joseph Fourier introduced the so-called trigonometric series in his investigations of heat flow. 

Thermodynamics
The gas laws, beginning with the inception of Boyle’s law in circa 1657, were the first basic thermodynamic functions.

The first main principle and second main principle, developed by Rudolf Clausius from 1850 to 1865, are the two core thermodynamic functions.

The logic of deriving new thermodynamic functions was said to have arisen out of the need to deduce values and interpretations for the entropy and internal energy, which in themselves lack a means of direct physical interpretation or quantification.

The ‘idea’ behind these types of new thermodynamic functions, supposedly, was said to have been first suggested in 1869 by French engineer Francois Massieu as explained in his “characteristic function” as he called it or Massieu functions, as they are called now.