Temperature is derivative of internal energy

Temperature of a thermodynamic system can be found when internal energy is known as a function of entropy.

Links:

  1. Wikipedia.

temperature

temperature of the system.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

entropy

entropy of the system.

Symbol:

S

Latex:

\(S\)

Dimension:

energy/temperature

volume

volume of the system.

Symbol:

V

Latex:

\(V\)

Dimension:

volume

particle_count

particle_count of the system.

Symbol:

N

Latex:

\(N\)

Dimension:

dimensionless

internal_energy

internal_energy of the system as a function of its natural variables.

Symbol:

U(S, V, N)

Latex:

\(U{\left(S,V,N \right)}\)

Dimension:

energy

law

T = Derivative(U(S, V, N), S)

Latex:
\[T = \frac{\partial}{\partial S} U{\left(S,V,N \right)}\]