In an earlier paper, we applied a procedure combining the energy difference method with a modified Kirkwood-Buff fluctuation theory to extrapolate chemical potential differences in three directions (T, P, x). The results showed that the extrapolations in pressure and concentration were successful and the linear temperature extrapolations were moderate in determination of the phase separations. In this paper we have tried to calculate the second order of the temperature dependence of the chemical potential difference using the energy difference methods of single-step and multistep switchings. Due to large fluctuations in calculation of the second orders, the method can only predict qualitatively or semiquantitatively the second-order terms.