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-rw-r--r--source/know/concept/maxwell-relations/index.md14
1 files changed, 11 insertions, 3 deletions
diff --git a/source/know/concept/maxwell-relations/index.md b/source/know/concept/maxwell-relations/index.md
index 892ced1..f51acea 100644
--- a/source/know/concept/maxwell-relations/index.md
+++ b/source/know/concept/maxwell-relations/index.md
@@ -9,7 +9,7 @@ layout: "concept"
---
The **Maxwell relations** are a useful set of relations in thermodynamics.
-They arise from the fact that the order of differentiation is irrelevant
+They arise from the fact that the ordering of differentiation is irrelevant
for well-behaved functions (sometimes known as the *Schwarz theorem*),
applied to the [thermodynamic potentials](/know/concept/thermodynamic-potential/).
@@ -54,7 +54,7 @@ $$\begin{aligned}
= \Big( \pdv{B}{x} \Big)_y^{-1}
\end{aligned}$$
-The following quantities are useful to rewrite some of the Maxwell relations:
+The following quantities can be 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 $$\kappa_S$$,
@@ -73,6 +73,10 @@ $$\begin{gathered}
C_P \equiv T \Big( \pdv{S}{T} \Big)_{P,N}
\end{gathered}$$
+But for simplicity and brevity,
+we will not do any such rewriting in this article.
+
+
## Internal energy
@@ -116,6 +120,7 @@ $$\begin{gathered}
\end{gathered}$$
+
## Enthalpy
The following Maxwell relations can be derived
@@ -158,6 +163,7 @@ $$\begin{gathered}
\end{gathered}$$
+
## Helmholtz free energy
The following Maxwell relations can be derived
@@ -200,6 +206,7 @@ $$\begin{gathered}
\end{gathered}$$
+
## Gibbs free energy
The following Maxwell relations can be derived
@@ -242,10 +249,11 @@ $$\begin{gathered}
\end{gathered}$$
+
## Landau potential
The following Maxwell relations can be derived
-from the Gibbs free energy $$\Omega(T, V, \mu)$$:
+from the Landau potential $$\Omega(T, V, \mu)$$:
$$\begin{gathered}
- \mpdv{\Omega}{V}{T} =