Abstract
In the preceding chapter titled, “Zeroth Law Revisited; Motive Forces; Thermodynamic Stability,” we examined some issues that pertain to thermodynamic motive forces. Also, some matters relating to intrinsic thermodynamic stability were investigated. These analyses were guided by the extremum principles for the internal energy and the entropy. In Chap. 10, other extremum principles are also identified and their consequences predicted.
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- 1.
Note, however, that while the relative size of the two phases does indeed depend upon the thermodynamic state of the system, their total mass does not, because it is necessarily conserved.
- 2.
Refer again to the chapter titled “Equilibrium, Motive Forces, and Stability” where issues of thermodynamic stability were investigated.
- 3.
Similar work in the entropy representation is also possible. The relevant potentials are then called Massieu functions. See appendix I for details.
- 4.
What constitutes a “thermodynamic potential” is dealt with later in this chapter.
- 5.
Recall that, in the preceding two chapters, the internal energy was shown to play a central role in the description of thermodynamic equilibrium and stability.
- 6.
Compare (8.5).
- 7.
That was first given in (5.6).
- 8.
Reader: Please note the procedure: To transform out of ( + t ds) we need to add ( − t s) to the primary function.
- 9.
Literally, this implies that its integral, or equivalently the sum, Δw′(t) is constant. Hence, w′ in both the states i and j is the same.
- 10.
Note that Δw′, etc., indicate that the changes being described may have occurred either wholly or partially non-quasi-statically.
- 11.
Again to be called the Gibbs potential, or equivalently, the Gibbs free energy, but note that in this sub-section the system being treated has both μ and \(\mathcal{Y}\) absent.
- 12.
Note the absence of the prime in the quantity (g i − g j ).
- 13.
Incidentally, such a potential was first introduced in (3.54) where it was equated to u + p v and named the Enthalpy.
- 14.
These variables are, of course, (v, t) and (p, t), respectively.
- 15.
See the chapter entitled:“Zeroth Law Revisited; Motive Forces; Thermodynamic Stability.”
- 16.
It was recommended there that “Because the reader has not yet been introduced to the Gibbs free energy, upon first reading a beginner might postpone the reading of that section until after the Gibbs potential had been introduced and fully discussed. Equation (6.52) and the development of (6.55) will become more clear after the Gibbs free energy has been properly introduced and fully explained. See (10.31)–(10.44).”
- 17.
The temperature t is maintained by contact with a heat energy reservoir.
- 18.
The pressure p is maintained by contact with a so-called volume reservoir.
- 19.
An exception, usually cited, is liquid Helium at ≈ 0.3 K.
- 20.
See Sears and Salinger, op. cit., pages 194–196.
- 21.
See (10.44).
- 22.
Therefore, the relative composition in all the phases is exactly known. It is exactly one!
- 23.
Physics for treating the boiling of water has not been included here. So this statement is valid only as long as the temperature is above the freezing point but below the boiling point of water.
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Tahir-Kheli, R. (2012). Energy and Entropy Extrema; Legendre Transformations; Thermodynamic Potentials; Clausius–Clapeyron Equation; Gibbs Phase Rule. In: General and Statistical Thermodynamics. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21481-3_10
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