Oct. 21 2002 : Lecture 18:

Describing the State of an Alloy

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Virtual Variations

Figure 18-1: Example of one particular choice of a virtual variation of a system. The originally homogeneous system is compared to two other systems of different size.

Question: Because they are extensive, shouldn't the internal energy in Figure 18-1 scale linearly with the volume?

Figure 18-2: Example of why it is not sufficient to consider variations like $\Delta U = U_o + U' \Delta V + U'' \Delta V^2/2 + \ldots$

Equilibrium: $(\ensuremath{\delta}S)_{\ensuremath{\delta}U = 0 \;, \; \ensuremath{\delta}V = 0} \leq 0$

Equilibrium: $(\ensuremath{\delta}U)_{\ensuremath{\delta}S = 0 \;, \; \ensuremath{\delta}V = 0} \geq 0$

$P$ and $T$ are Uniform when Volume and Energy can be Exchanged

Figure 18-3: Three separate systems that are in mechanical equilbrium, but not necessarily thermal equilibrium.