The first differential of equation (10.4.5.2) is

          (9.3)

The various partial derivatives appearing in the foregoing equation recur so frequently that it is convenient to introduce special symbols for them.  They are called intensive parameters.

relation temperature                  

relation pressure                                   

relation entity potential               

With this notation equation (10.4.6.1) becomes

Equation (9.3) is said to be the energetic fundamental relation, with energetic extensive parameters S, V, N₁...N_r and energetic intensive parameters T, P, μ₁...μ_r.  Thermodynamic analysis carried out with this set of parameters is said to be in the energy representation, i.e., the energy is the dependent variable and the entropy is an independent variable.

Equation (9.1) is said to be the entropic fundamental relation, with entropic extensive parameters E, V, N₁...N_r.  By taking the first differential, one can obtain the following entropic intensive parameters.

Thermodynamic analysis carried out with this set of parameters is said to be in the entropy representation, i.e., the entropy is the dependent variable and the energy is an independent variable.

Staying in the energy representation it is desirable to define

as relation thermal or heat flux.

       as relation volume change or relation mechanical work.

  as relation entity change or population work.

I can now write equation (10.3) as

                                                              (9.4)

Equation (9.3) can be interpreted as saying that a change in relation energy of a system can occur as a result of a flux of heat dQ, mechanical work dW_m, or population work dW_e.

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