next up previous
Next: Partition Function and Free Up: Probabilities of Macroscopic States. Previous: Canonical Ensemble


Statistical Mechanics and Thermodynamics


Let us change the volume reversible . Then $S=\mathit{const}$. We define pressure as

P = -\left(\frac{\partial E}{\partial V}\right)_S\end{displaymath}

In the definition of temperature we implicitly held $V=\mathit{const}$:

\frac1T = \left(\frac{\partial S}{\partial E}\right)_V
 T = \left(\frac{\partial E}{\partial S}\right)_V\end{displaymath}

 dE = T\,dS - P\,dV\end{displaymath} (4)

Heat and Entropy

What do we know about heat from Thermodynamics?

There is ``entropy'' S'. In closed systems $\Delta
 S'=0$ for reversible processes and $\Delta S'\gt$ for irreversible processes (Second Law)
Energy is conserved: for reversible processes in open systems $\Delta E = T\Delta S' - P\Delta V$ (First Law)
What did we found about our entropy $S=k\ln W$? Exactly same things!
These things are same: S=S'.
Meaning of the Boltzmann Constant:
If we defined entropy as $\ln W$, temperature would have dimension of energy. We measure temperature differently--and must pay for it by adding a constant!

We can prove all postulates of thermodynamics from statistics!

© 1997 Boris Veytsman and Michael Kotelyanskii
Thu Sep 4 21:28:23 EDT 1997