Thermodynamic variables versus microscopic variables

A primary goal of this course is the description, characterization, and hopefully the prediction of the properties and behaviors of a real material. Of course, any description or characterization requires a certain amount of forethought about the lexicon that will be used. Our lexicon involves the variables that will efficiently describe the properties of materials.

Question: What kinds of variables describe a material body and the changes that occur as it is manipulated

How does one describe a body or a system completely? There are at least two plausible approaches:

Method of description: 1

Describe for each particle in the body

• position $(x,y,z)$
• velocity $(V_x,V_y,V_Z)$
• charge $q$
• spin
  $\vdots$
• etc.

Question: Why is Avogadro's number, $\ensuremath{\mbox{N}_{\mbox{avag.}}} \newcommand {\pascal}{... ...uremath{\mbox{mole}^{-1}}} \newcommand {\mole}{\ensuremath{\mbox{mole}}}$ so big?

Keeping track of $\ensuremath{\mbox{N}_{\mbox{avag.}}} \newcommand {\pascal}{... ...uremath{\mbox{mole}^{-1}}} \newcommand {\mole}{\ensuremath{\mbox{mole}}}$ molecules is just not humanly (or even, in this decade at least, computerly) possible.

Method of description: 2

Determine a quantity that reflects the average or sum total properties of the body

Examples:

1. Volume $V$

2. Total number of atoms of type A, $N_A$

3. Total number of B-molecules $N_B$

4. Total charge

5. Size of system?

   
   

6. charge per volume.

Question: Can you identify others?

Question: If an applied force, $F$, tries to make a spring get shorter (larger opposing forces $\rightarrow$ shorter spring)--what is it that makes the volume of a body get smaller?

How would you measure pressure?

Design a small gauge:

Figure 3-1: A small pressure gauge: use $\ensuremath {{x}_\circ }$ to measure $P$.

$$\input{equations/newtonp}$$ (03-1)

Compression, caused by large positive pressures, compresses the spring. In other words, a negative force in a spring is compressive; thus pressure and force have different sign conventions. Tensile forces extend the spring and are associated with negative pressures.¹

What kinds of things might be wrong with our little device to cause it to give bad measurements of pressure?

Imagine that we made our device very small. In the limit of an infinitely small device, we could use it to measure pressure from point to point: $P(\vec{x})$.

Question: Practically, how small would be too small?

Question: Would two bodies be in equilibrium if they were in mechanical contact and their pressures are different?

Question: Are pressure and volume similar variables? How are they naturally coupled?