Solution
= Solution
For the symmetric <regular solution model>, the dimensionless mixing <free energy> is $f/(k_BT)=\phi\log\phi+(1-\phi)\log(1-\phi)+\chi\phi(1-\phi)$. At the <thermodynamic critical point>, its second and third <derivatives> in composition vanish. The third derivative gives $\phi_c=1/2$; the second then gives $4-2\chi_c=0$. Therefore
$$
\boxed{\chi_c=2,\qquad T_c=600\ \mathrm K/2=300\ \mathrm K.}
$$
This uses the equal-size, composition-symmetric mixture model.