In thermodynamics, a

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:

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

where

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

References

1. Perrot, Pierre. (1998).

2. Richet, Pascal. (2001).

**tension**, symbol*X*, is a partial derivative of the internal energy*U*with respect to an extensity, symbol*x*, other extensive quantities being kept constant. [1] Subsequently, with any extensity*xi*it is always possible to associate a tension variable*Xi*: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

*T*and*P*are the tensions and*S*and*V*are the extensities. To restate, the measure of pressure*P*, for instance, is a quantity of tension whose conjugated extensity is volume*V*. In the case of transfer, an amount of energy in the form of pressure-volume work*dW*can be exchanged between two interactive systems (the body of steam, for example, and the body of surrounding atmosphere):where the minus sign is the consequence of the "system-based" sign convention of

*dW*> 0 if*dV*< 0.References

1. Perrot, Pierre. (1998).

*A to Z of Thermodynamics.*Oxford: Oxford University Press.2. Richet, Pascal. (2001).

*The Physical Basis of Thermodynamics: with Applications to Chemistry,*(pg. 11). Springer.