The heat balance of a system is shown as:

Heat removed from the solution $=$ Heat lost from the solution

$E{w}_1=yq+C_p[(1+c_1)w_1](T_1-T_2)$

Where,

$$ the latent heat of vaporisation $(\frac{J}{k}g)$

q the latent heat of crystallisation $(\frac{J}{k}g)$

$T_{1,2}$ the initial and final temperatures of the solution $($K$)$

$C_p$ the heat capacity of the solution $($J$/$kg$.$C$)$

Show that

$E=\frac{q{R}_m(c_1-c_2)+C_p(T_1-T_2)(1+c_1)[1-c_2(R_m-1)]}{[1-c_2(R_m-1)]-q{R}_m{c}_2}$