Characteristic function (thermodynamic)

In Thermodynamic, a characteristic function indicates a function of state expressed with the assistance two parameters specified well, which, with it only, entirely characterizes the studied pure substance.

Are characteristic functions:

energy interns U = U (V, S, NR) well by the theorem of the implicit functions S (U, V, NR), but it is a less practical function;

the enthalpy H = H (p, S, NR);

free energy F = F (V, T, NR);

free enthalpy G = G (p, T, NR);

the latter is that which is tabulée. One will focus oneself on this function.

Caution: not to confuse the functions H, F and G with the thermodynamic Potential H°= U + p°.V; F° = U-T°.S; the exergie G° = U +p°.V - T°.S

Free enthalpy G (p, T, NR)

One immediately notices because of the extensive property of G that G (p, T, NR) = NR G (p, T, 1) or = N/ $N_A$ .G (p, T, $N_A$ ). One will reason with NR constant. Exit NR.

That is to say G (p, T) and its differential dG = V .dp - S .dT.

The data of G (p, T) thus gives V = V (p, T), i.e. the EQUATION of STATE and thus all the coefficients thermoelastic. It gives also S (p, T). One can thus draw from it H (p, T) = G +T.S; F (p, T) = G - p.V; and U (p, T) = G +T.S - p.V; i.e. VERY parameterized out of p and T: G (p, T) is thus well a characteristic function.

Evaluation of the thermodynamic tables G (p, T, $N_A$ )

if the free enthalpy is selected it is because its experimental evaluation is “relatively” easy.

1. His associated perfect gas is very known (cf Perfect gas) 2. His equation of state in experiments is known. Thus one can numerically find $C_p (p, T)$ starting from C° (T). 3. One can then evaluate the difference between G (p, T) and the free enthalpy of associated perfect gas: it is what one tabule.

Often the equation of state is given in the form of Z: = PV/RT = F (p, T). Then the correction is evaluated “enough” easily according to Z.Les tables give this correction.

4. If one knows well the phase shift liquid-gas, i.e. the experimental curve of triple point, steam pressure $p_S (T)$ at the critical point, AND the latent heat of vaporization L (T), then one can draw up the tables of G (p, T) of the liquid (in general with less precision!).

5. One repeats the process for crystallization, and then one obtains G (p, T) solid. That can give rather precise results until the low temperatures. In lower part of the triple point, the curve to be considered is that of sublimation, but the process is the same one. One must find that S (p, T) tends towards zero when T->0K.

An example: argon

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this fluid is interesting because simple of structure. It resembles much a GPM (cf Perfect gas). The corrections are minor except of course with the approach of liquefaction. One can in addition numerically simulate argon-computed using thousands of small balls in interaction (obviously not question of taking a mole of it!). One tests the capability of thermodynamics thus.

A less simple example water

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in fact water is in oneself a fascinating object of thermodynamics. Moreover it is THE FLUID in the heat engines. Finally it is with the air, the essential component of our biosphere. And of course in don't chemistry and biochemistry, its properties thermodynamic cease astonishing, because living it evolved/moved to adapt (“while adapting” would be more correct, not?) with thermodynamics air and water.

See too

Transform of Legendre | Potential thermodynamic