Intensive Variable | Extensive Variable | Energy | Function | Product | Person | |

Pressure P | Volume dV | pressure-volume work | δW | pdV | Clapeyron (1834) | |

Temperature T | Entropy dS | internal work (transformational content energy) | δQ | TdS | Clausius (1865) | |

Chemical potential μ | Particle number dn | species transfer work | μdn | Gibbs (1876) | ||

Force F | Length dx | stress-strain work | Fdx | Hooke (1660) | ||

Electromotive force ε | Charge de | electrical work | εde | Gibbs (1876) - Helmholtz (1882) | ||

Surface tension γ (superficial tension σ) | Surface area dA(area of surface considered s) | surface work | γdA (σδs) | Gibbs (1876) | ||

Gravitational potential ψ | Mass dm | gravitation work | ψdm | |||

Electric field E | Electric dipole moment dp | electric polarization | Edp | |||

Magnetic field B | Magnetic moment dm | magnetic polarization | Bdm |

The general use of the conjugate pairs perspective is that one can quantify the internal energy of a system as the sum of the conjugate variables. In short, with any extensity

which is called the "conjugate", whereby, according to the first law, the change in internal energy

The right side of this expression is what is called a Pfaffian form. To give a simple example, in the process whereby an indefinitely small quantity of heat

which is the first and the second law of thermodynamics combined into an analysis of the process. [3]

History

It is difficult to track down the origin of this topic, although it might be derived from the

One of the first to summarize this as a “work principle” seems to have been Danish physical chemist Johannes Bronsted who in a 1946 monograph, reprinted in 1955 as

in which

References

1. (a) Attard, Phil. (2002).

(b) Alberty, Robert, A. (2003).

2. Brønsted, Johannes. (1955).

3. Clausius, Rudolf. (1879).

4. Kirkwood, J.G. and Oppennheim, Irwin. (1961).

Further reading

● Foss, O. (1948). “The Brønsted Work Principle: Thermoelectric, Galvanic and Thermo-Chemical”,

● LaMer, V.K., Foss, O., and Reiss, H. (1949). “Some New Prodcedures in Thermodynamic Theory Inspired by the Recent Work of J.N. Bronsted.”

● MacRae, D. (1955). “Brønsted's Work Principle

● MacDougal, F.H. (1940). “Brønsted's Criticism of Classical Thermodynamics.”

● Thims, Libb. (2007).

External links

● Conjugate variables (thermodynamics) – Wikipedia.