We have carried out a comprehensive study of a truncated Lennard-Jones (TRLJ) system (potential cutoff = 2.5 sigma) in the Percus-Yevick (PY) approximation using Baxter’s equations and algorithms with some degree of novelty. We have determined the liquid-vapor phase diagram from the "energy equation of state," have determined the spinodal curve for the compressibility equation of state, and have made calculations of the energy, compressibility, and virial pressures. We have calculated heat capacities, examined their extrema for the energy and compressibility equations, and have contrasted them with previously published simulation data. Our "energy equation of state" is defined self-consistently within the PY approximation and differs from the definition of other authors.