Update 4_sommerfeld_model.md - minor fix in Cv estimate

src/4_sommerfeld_model.md

@@ -220,10 +220,10 @@ ax.set_xlabel(r"$\varepsilon$")
 draw_classic_axes(ax, xlabeloffset=.2)
 ```
 
-Electrons in the top triangle are being excited to the bottom triangle due to temperature increase. Number of excited electrons $\approx\frac{1}{2}g(\varepsilon_{\rm F})k_{\rm B}T=n_{\rm exc}$. Total extra energy $E(T)-E(0)=n_{\rm exc}k_{\rm B}T=\frac{1}{2}g(\varepsilon_{\rm F})k_{\rm B}^2T^2$.
+Electrons in the top triangle are being excited to the bottom triangle due to temperature increase. Number of excited electrons $\approx\frac{1}{4}g(\varepsilon_{\rm F})k_{\rm B}T=n_{\rm exc}$. Total extra energy $E(T)-E(0)=n_{\rm exc}k_{\rm B}T=\frac{1}{2}g(\varepsilon_{\rm F})k_{\rm B}^2T^2$.
 
 $$
-C_{V,e}=\frac{ {\rm d}E}{ {\rm d}T}=g(\varepsilon_{\rm F})k_{\rm B}^2T=\ ...\ =\frac{3}{2}Nk_{\rm B}\frac{T}{T_{\rm F}}\propto T
+C_{V,e}=\frac{ {\rm d}E}{ {\rm d}T}=\frac{1}{2}g(\varepsilon_{\rm F})k_{\rm B}^2T=\ ...\ =\frac{3}{4}Nk_{\rm B}\frac{T}{T_{\rm F}}\propto T
 $$
 
 $T_{\rm F}=\frac{\varepsilon_{\rm F}}{k_{\rm B}}$ is the _Fermi temperature_.