Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
on_phenomenological_thermodynamics_._note [2015/11/07 19:48] nikolaj |
on_phenomenological_thermodynamics_._note [2015/11/08 14:46] nikolaj |
||
|---|---|---|---|
| Line 42: | Line 42: | ||
| The fact that pressure and volume are then reciprocal, $p=\frac{c^ST}{V}$, leads to the occurrence of all the logarithms that are so typical for phenomenological thermodynamics (see below). E.g. in computing change of energies, we often must integrate external variables against internal ones. | The fact that pressure and volume are then reciprocal, $p=\frac{c^ST}{V}$, leads to the occurrence of all the logarithms that are so typical for phenomenological thermodynamics (see below). E.g. in computing change of energies, we often must integrate external variables against internal ones. | ||
| - | $(\Delta G)_{T,\{N_i\}}:=\int_{p_2}^{p_1}V(T,p)\,{\mathrm d}p=c^S T\ln(\frac{p_2}{p_1})\implies p_2 = p_1\cdot{\mathrm e}^{\frac{(\Delta G)_{T,\{N_i\}}}{c^S T}}$. | + | $(\Delta G)_{T,\{N_i\}}:=\int_{p_2}^{p_1}V(T,p)\,{\mathrm d}p=c^S T\ln(\frac{p_2}{p_1})$ |
| + | |||
| + | $\implies p_1 = p_2\cdot\exp\left(-\dfrac{(\Delta G)_{T,\{N_i\}}}{c^S T}\right)$. | ||
| This sort of "concentration varies with $\exp(-E/k_BT)$" equation also pops up often in chemistry and electronics (Goldmann equation, Nernst equation, diode current-voltage-characteristics,...) | This sort of "concentration varies with $\exp(-E/k_BT)$" equation also pops up often in chemistry and electronics (Goldmann equation, Nernst equation, diode current-voltage-characteristics,...) | ||
| Line 58: | Line 60: | ||
| ----- | ----- | ||
| === Related === | === Related === | ||
| + | [[Notes on physical theories . note]], | ||
| [[Statistical internal energy]] | [[Statistical internal energy]] | ||
