From a39bb3b8aab1aeb4fceaedc54c756703819776c3 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sat, 17 Dec 2022 18:19:26 +0100
Subject: Rewrite "Lagrange multiplier", various improvements

---
 source/know/concept/thermodynamic-potential/index.md | 10 ++++++++--
 1 file changed, 8 insertions(+), 2 deletions(-)

(limited to 'source/know/concept/thermodynamic-potential')

diff --git a/source/know/concept/thermodynamic-potential/index.md b/source/know/concept/thermodynamic-potential/index.md
index ece1551..b3bedda 100644
--- a/source/know/concept/thermodynamic-potential/index.md
+++ b/source/know/concept/thermodynamic-potential/index.md
@@ -15,8 +15,8 @@ Such functions are either energies (hence *potential*) or entropies.
 Which potential (of many) decides the equilibrium states for a given system?
 That depends which variables are assumed to already be in automatic equilibrium.
 Such variables are known as the **natural variables** of that potential.
-For example, if a system can freely exchange heat with its surroundings,
-and is consequently assumed to be at the same temperature $$T = T_{\mathrm{sur}}$$,
+For example, if a system can freely exchange heat with its environment,
+and is consequently assumed to be at the same temperature $$T = T_{\mathrm{env}}$$,
 then $$T$$ must be a natural variable.
 
 The link from natural variables to potentials
@@ -32,6 +32,7 @@ Mathematically, the potentials are related to each other
 by [Legendre transformation](/know/concept/legendre-transform/).
 
 
+
 ## Internal energy
 
 The **internal energy** $$U$$ represents
@@ -76,6 +77,7 @@ to help keep track of which function depends on which variables.
 They are meaningless; these are normal partial derivatives.
 
 
+
 ## Enthalpy
 
 The **enthalpy** $$H$$ of a system, in units of energy,
@@ -115,6 +117,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 
+
 ## Helmholtz free energy
 
 The **Helmholtz free energy** $$F$$ represents
@@ -154,6 +157,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 
+
 ## Gibbs free energy
 
 The **Gibbs free energy** $$G$$ represents
@@ -192,6 +196,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 
+
 ## Landau potential
 
 The **Landau potential** or **grand potential** $$\Omega$$, in units of energy,
@@ -230,6 +235,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 
+
 ## Entropy
 
 The **entropy** $$S$$, in units of energy over temperature,
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