User:ScottTParker/Sandbox

$X_{micelle} = \frac{X_N}{N}$ $X 1$ $C = X_1 + X_N \$

$X_1=\left( \frac{C-X_1}{N} \right)^{1/N}e^{-\left(\mu_1^0-\mu_N^0 \right) /kT}$

$X_N=N \left[X_1e^{\left(\mu_1^0-\mu_N^0 \right) /kT} \right] ^N$

$C_{CMC}=\frac{2}{N^{1/(N-1)}K^{N/(N-1)}}$

$K=e^{\left(\mu_1^0-\mu_N^0 \right) /kT}$

$X = \frac{1}{A_{particle}}$

$P = \frac{k T}{N} \left[ C + (N-1) X_1 \right]$

$\pi = \frac{k T}{N} \left[ \frac{1}{(A-A_0)} + \frac{(N-1)}{(A_1-A_0)} \right]$

$(A_1-A_0) = (A - A_0) \left[ 1 + \left(\frac{2 (A_c-A_0)}{A_1-A_0} \right)^{N-1} \right]$

$E = E_{int} + E_{disp} + P A\$