Update documentation

Author: verga

pages/PS-free.html

@@ -274,7 +274,19 @@ <h3>Free particles: ideal boson and fermion&nbsp;gases</h3>
 S = \frac{E - \mu N - \Phi}{T} = -\left. \frac{\partial\Phi}{\partial T}\right|_z + \left. \frac{\mu z}{T^2} \frac{\partial \Phi}{\partial z}\right|_T = -\left. \frac{\partial \Phi(T,\mu)}{\partial T}\right|_{V,\mu}
 $$</div>
 <p>
-for the entropy. An immediate consequence of these formulas is that the ideal gas&nbsp;relation,
+for the&nbsp;entropy
+</p>
+<div class="math">$$
+S = \frac{5}{2} \frac{V}{\lambda^3}\Big(z + \frac{z^2}{2^{5/2}} \Big) - \frac{\mu}{T} \frac{V}{\lambda^3}\Big(z + \frac{z^2}{2^{3/2}} \Big)
+$$</div>
+<p>
+or&nbsp;equivalently
+</p>
+<div class="math">$$
+S = \frac{3}{2} \frac{V}{\lambda^3}\Big(z + \frac{z^2}{2^{5/2}} \Big)  - \frac{\mu N}{T} - \frac{\Phi}{T}.
+$$</div>
+<p>
+An immediate consequence of these formulas is that the ideal gas&nbsp;relation,
 </p>
 <div class="math">$$
 E = \frac{3}{2} PV