 Solution

For a hard disc configuration, the potential energy is zero if no particles overlap and infinite otherwise. All allowed configurations therefore have the same configurational Boltzmann factor. At fixed $N,A,T$, their relative free energies differ through the volume of accessible configuration space:The kinetic contribution is common to the phases at the same temperature. “Entropy-driven crystallization” does not mean that particles develop an energetic attraction; excluded volume changes the number of possible many-particle arrangements.