Definitions
Bulk modulus / compressibility
\[ B = \frac{1}{\kappa} = \frac{\Delta P}{ - \Delta V / V} \]
Energy
Entropy
Ideal gas
Surface area of n-dimensional hypersphere
\[ A = \frac{2\pi^{n/2}}{(\frac{n}{2}-1)!} r^{n-1} \]
N indistinguishable particles
\[ \Omega_1 = V \cdot V_p \]
\begin{align*}
\Omega_N & = \frac{1}{N!} \frac{V^N}{h^{3N}} \times \frac{2\pi^{3N/2}}{(\frac{N}{2}-1)!} (\sqrt{2mU})^{N-1} \\
& \approx \frac{1}{N!} \frac{V^N}{h^{3N}} \frac{\pi^{3N/2}}{(\frac{N}{2})!} (\sqrt{2mU})^{N}
\end{align*}
\[ \Omega_N = f(N) V^N U^{3N/2} \]
Sackur-Tetrode equation
\[ S = Nk \left[\ln\left(\frac{V}{N}\left(\frac{4\pi m U}{3 N h^2}\right)^{3/2} \right) + \frac{5}{2}\right] \]