Internal energy differential

The fundamental thermodynamic relations are fundamental equations which demonstrate how important thermodynamic quantities depend on variables that are measurable experimentally.

Notation:

1. \(d\) denotes an exact, path-independent differential.

Notes:

1. Entropy, volume, and particle count are so called natural variables of internal energy as a thermodynamic potential.

2. For a system with more than one type of particles, the last term can be represented as a sum over all types of particles, i.e. \(\sum_i \mu_i \, d N_i\).

Conditions:

1. The system is in thermal equilibrium with its surroundings

2. The system is composed of only one type of particles, i.e. the system is a pure substance.

Links:

1. Wikipedia.

internal_energy_change

Infinitesimal change in internal_energy of the system.

Symbol:

dU

Latex:

\(dU\)

Dimension:

energy

temperature

temperature of the system.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

entropy_change

Infinitesimal change in entropy of the system.

Symbol:

dS

Latex:

\(dS\)

Dimension:

energy/temperature

pressure

pressure inside the system.

Symbol:

p

Latex:

\(p\)

Dimension:

pressure

volume_change

Infinitesimal change in volume of the system.

Symbol:

dV

Latex:

\(dV\)

Dimension:

volume

chemical_potential

chemical_potential of the system.

Symbol:

mu

Latex:

\(\mu\)

Dimension:

energy

particle_count_change

Infinitesimal change in the number of particles in the system.

Symbol:

dN

Latex:

\(dN\)

Dimension:

dimensionless

law

dU = T * dS - p * dV + mu * dN

Latex:

\[dU = T dS - p dV + \mu dN\]