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authorPrefetch2022-10-20 18:25:31 +0200
committerPrefetch2022-10-20 18:25:31 +0200
commit16555851b6514a736c5c9d8e73de7da7fc9b6288 (patch)
tree76b8bfd30f8941d0d85365990bcdbc5d0643cabc /source/know/concept/maxwell-relations
parente5b9bce79b68a68ddd2e51daa16d2fea73b84fdb (diff)
Migrate from 'jekyll-katex' to 'kramdown-math-sskatex'
Diffstat (limited to 'source/know/concept/maxwell-relations')
-rw-r--r--source/know/concept/maxwell-relations/index.md30
1 files changed, 15 insertions, 15 deletions
diff --git a/source/know/concept/maxwell-relations/index.md b/source/know/concept/maxwell-relations/index.md
index aa51b06..892ced1 100644
--- a/source/know/concept/maxwell-relations/index.md
+++ b/source/know/concept/maxwell-relations/index.md
@@ -14,15 +14,15 @@ for well-behaved functions (sometimes known as the *Schwarz theorem*),
applied to the [thermodynamic potentials](/know/concept/thermodynamic-potential/).
We start by proving the general "recipe".
-Given that the differential element of some $z$ is defined in terms of
-two constant quantities $A$ and $B$ and two independent variables $x$ and $y$:
+Given that the differential element of some $$z$$ is defined in terms of
+two constant quantities $$A$$ and $$B$$ and two independent variables $$x$$ and $$y$$:
$$\begin{aligned}
\dd{z} \equiv A \dd{x} + B \dd{y}
\end{aligned}$$
-Then the quantities $A$ and $B$ can be extracted
-by dividing by $\dd{x}$ and $\dd{y}$ respectively:
+Then the quantities $$A$$ and $$B$$ can be extracted
+by dividing by $$\dd{x}$$ and $$\dd{y}$$ respectively:
$$\begin{aligned}
A = \Big( \pdv{z}{x} \Big)_y
@@ -30,7 +30,7 @@ $$\begin{aligned}
B = \Big( \pdv{z}{y} \Big)_x
\end{aligned}$$
-By differentiating $A$ and $B$,
+By differentiating $$A$$ and $$B$$,
and using that the order of differentiation is irrelevant, we find:
$$\begin{aligned}
@@ -55,11 +55,11 @@ $$\begin{aligned}
\end{aligned}$$
The following quantities are useful to rewrite some of the Maxwell relations:
-the iso-$P$ thermal expansion coefficient $\alpha$,
-the iso-$T$ combressibility $\kappa_T$,
-the iso-$S$ combressibility $\kappa_S$,
-the iso-$V$ heat capacity $C_V$,
-and the iso-$P$ heat capacity $C_P$:
+the iso-$$P$$ thermal expansion coefficient $$\alpha$$,
+the iso-$$T$$ combressibility $$\kappa_T$$,
+the iso-$$S$$ combressibility $$\kappa_S$$,
+the iso-$$V$$ heat capacity $$C_V$$,
+and the iso-$$P$$ heat capacity $$C_P$$:
$$\begin{gathered}
\alpha \equiv \frac{1}{V} \Big( \pdv{V}{T} \Big)_{P,N}
@@ -77,7 +77,7 @@ $$\begin{gathered}
## Internal energy
The following Maxwell relations can be derived
-from the internal energy $U(S, V, N)$:
+from the internal energy $$U(S, V, N)$$:
$$\begin{gathered}
\mpdv{U}{V}{S} =
@@ -119,7 +119,7 @@ $$\begin{gathered}
## Enthalpy
The following Maxwell relations can be derived
-from the enthalpy $H(S, P, N)$:
+from the enthalpy $$H(S, P, N)$$:
$$\begin{gathered}
\mpdv{H}{P}{S} =
@@ -161,7 +161,7 @@ $$\begin{gathered}
## Helmholtz free energy
The following Maxwell relations can be derived
-from the Helmholtz free energy $F(T, V, N)$:
+from the Helmholtz free energy $$F(T, V, N)$$:
$$\begin{gathered}
- \mpdv{F}{V}{T} =
@@ -203,7 +203,7 @@ $$\begin{gathered}
## Gibbs free energy
The following Maxwell relations can be derived
-from the Gibbs free energy $G(T, P, N)$:
+from the Gibbs free energy $$G(T, P, N)$$:
$$\begin{gathered}
\mpdv{G}{T}{P} =
@@ -245,7 +245,7 @@ $$\begin{gathered}
## Landau potential
The following Maxwell relations can be derived
-from the Gibbs free energy $\Omega(T, V, \mu)$:
+from the Gibbs free energy $$\Omega(T, V, \mu)$$:
$$\begin{gathered}
- \mpdv{\Omega}{V}{T} =