Internal energy is first order homogeneous function¶

Internal energy is a first-order homogeneous function of its internal variables (entropy, volume, and particle count).

Links:

Wikipedia, first equation.

entropy¶: entropy.

Symbol:: S
Latex:: \(S\)
Dimension:: energy/temperature

volume¶: volume

Symbol:: V
Latex:: \(V\)
Dimension:: volume

particle_count¶: particle_count.

Symbol:: N
Latex:: \(N\)
Dimension:: dimensionless

internal_energy¶: internal_energy as a function of entropy, volume, and particle_count.

Symbol:: U(S, V, N)
Latex:: \(U{\left(S,V,N \right)}\)
Dimension:: energy

factor¶: Dimensionless real-valued factor.

Symbol:: k
Latex:: \(k\)
Dimension:: dimensionless

homogeneity_condition¶

U(k * S, k * V, k * N) = k * U(S, V, N)

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