  We develop an ansatz for expressing the free energy of the two dimensional
$q$-states Potts model for $q > 4$ near its first order phase transition point.
We notice that for the moderate values of $ q \lesssim 15 $, the energy profile
at the phase transition is not expressible as a sum of gaussians. We discuss
how this affects the traditional finite size analysis of this phase transition.
In particular, the dominant length scale governing the finite size corrections
turns out to be much (${} \sim 6$ ~times) larger than the largest correlation
length in the problem.
