which is called the conjugate. As such, according to the first law, the change in internal energy of a system is given by:

Stated verbially, extensity is an energy “transfer variable”, defined such that when two systems A and B are brought into contact or interact, the assembly (A + B) being isolated, each system having different tensions, an exchange of energy results via a transfer of an extensity, such that the transfer ends when the tensions have equalized. [2]

First law example

The simplest example being the addition of a quantity of heat δQ to a body, whereby the body expands, according to Boerhaave's law, pushing outward on the surrounding atmosphere, thus doing an amount of pressure volume work δW. The first law thus gives:

dU = δQ – δW

or stated in terms of conjugate variables (with substitution of the integrating factor formulation of heat and work):

dU =Tds–Pdv

where

where the minus sign is the consequence of the "system-based" sign convention of

References

1. Perrot, Pierre. (1998).

2. Richet, Pascal. (2001).