Enthalpy of mixing of a non-ideal solution I have this equation of Flory–Huggins model:
$$\Delta_\mathrm{mix}G = RT(n_1\ln\phi_1 + n_2\ln\phi_2) + \chi n_1\phi_2,$$
where $\phi$ is the volume fraction, $n$ is the amount of substance and $\chi$ is the parameter of solvent-polymer processing that depends only on temperature.
I need an expression for $\Delta_\mathrm{mix}H.$
There are two ways (at least) to solve this:
(1) Evaluate $\Delta S = -\left( \frac{\partial \Delta G}{\partial T} \right)_{p,n} $
and add $T\Delta S$ to $\Delta G$.
or
(1) Evaluate directly $\Delta H = -T^2 \left( \frac{\partial (\Delta G/T)}{\partial T} \right)_{p,n} $
Either way I obtained the result
$\Delta H = \chi n_1 \phi_2 - n_1\phi_2 T \left( \frac{\partial \chi }{\partial T} \right)_{p,n} $