Abstract
The first row of boxes shown in Fig. 3.1 depicts a number of identical systems differing only in their internal energies, \(E_\nu \), volumes, \(V_\nu \), and mass contents, \(n_\nu \). The boundaries of the systems allow the exchange of these quantities between the systems upon contact. The second row of boxes in Fig. 3.1 illustrates this situation. All (sub-)systems combined form an isolated system. We ask the following question: What can be said about the quantities \(x_\nu \), where \(x\) represents \(E\), \(V\) or \(n\), after we bring the boxes into contact and allow the exchanges to occur?
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The conditions (3.16) are mathematical statements of Le Châtelier’s principle, i.e. driving a system away from its stable equilibrium causes internal processes tending to restore the equilibrium state.
- 2.
Thermodynamics does not predict the states of matter or describe their structure. Their existence, here gas and liquid, is an experimental fact, which we use at this point.
- 3.
We shall show how to calculate this curve on the basis of a microscopic interaction model—the van der Waals theory.
- 4.
The meaning of \(A\) and \(B\) can of course be interchanged.
- 5.
The system is methane gas adsorbing on the graphite basal plane located at \(z=0\). A computer program generating profiles like these is included in the appendix. The theoretical background needed to understand the program is discussed in Chap. 6.
- 6.
In these units the gas pressure in Fig. 3.11 is \(P=0.04\). The temperatures from top to bottom are \(T=2.0,1.2, 1.05\).
- 7.
We return to Fig. 3.11 in an example starting on p. 207.
- 8.
Potentially this may be disturbing. According to the steps leading from Eq. (2.164) to Eq. (2.165) one may be led to conclude that \(G=0\) all the time and everything falls apart. However this reasoning confuses two very different situations. Inequality (3.68) means that we prepare a system subject to certain thermodynamic conditions \(T\) and \(P\) and leave this system alone until no further change is observed. This fixes the equilibrium value of the free enthalpy, \(G\), for a particular pair \(T,P\). Repeating this procedure for many \(T,P\)-pairs we map out the equilibrium values of \(G\) above the \(T\)-\(P\)-plane (cf. Fig. 2.13). With this function \(G=G(T,P)\) or \(G=G(T,P,n)\) we now can do calculations, differentiating or integrating, involving \(T\), \(P\), \(n\) and possibly other variables. This is how we have obtained the Eqs. (2.164) and (2.165). Therefore there is no problem here!
- 9.
Peter Debye, Nobel prize in chemistry for his many contributions to the theory of molecular structure and interactions, 1936.
- 10.
This also is something to keep in mind when buying a new washing machine. A higher spin speed is usually better, because of the decreased residual water content in the laundry. This water must be evaporated in the dryer, and the enthalpy of evaporation again is considerable. On the other hand, a modern condenser dryer often is capable of reclaiming some of the invested energy upon condensation.
- 11.
More precisely, the process comes to a halt at coexistence of ice and liquid water.
- 12.
Under “pool conditions” the sun transfers heat to the contents of our glass and the melting continues until the ice is gone.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hentschke, R. (2014). Equilibrium and Stability. In: Thermodynamics. Undergraduate Lecture Notes in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36711-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-36711-3_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36710-6
Online ISBN: 978-3-642-36711-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)