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1 files changed, 17 insertions, 1 deletions

diff --git a/content/know/concept/two-fluid-equations/index.pdc b/content/know/concept/two-fluid-equations/index.pdc
index df45e73..9ae9dbf 100644
--- a/content/know/concept/two-fluid-equations/index.pdc
+++ b/content/know/concept/two-fluid-equations/index.pdc
@@ -129,7 +129,7 @@ $$\begin{aligned}
 Now we have 14 equations, so we need 2 more, for the pressures $p_i$ and $p_e$.
 This turns out to be the thermodynamic **equation of state**:
 for quasistatic, reversible, adiabatic compression
-of a gas with constant heat capacities (i.e. a *calorically perfect* gas),
+of a gas with constant heat capacity (i.e. a *calorically perfect* gas),
 it turns out that:
 
 $$\begin{aligned}
@@ -168,6 +168,22 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
+Note that from the relation $p = C n^\gamma$,
+we can calculate the $\nabla p$ term in the momentum equation,
+using simple differentiation and the ideal gas law:
+
+$$\begin{aligned}
+    p = C n^\gamma
+    \quad \implies \quad
+    \nabla p
+    = \gamma \frac{C n^{\gamma}}{n} \nabla n
+    = \gamma p \frac{\nabla n}{n}
+    = \gamma k_B T \nabla n
+\end{aligned}$$
+
+Note that the ideal gas law was not used immediately,
+to allow for $\gamma \neq 1$.
+
 
 ## Fluid drifts