Recently, it was found that polymers follow the principle of temperature-pressure (T-P) superposition. This principle states the temperature insensitiveness of the shape of the configurational free energy. An analytical free energy for polymeric liquids is developed in the framework of the perturbation theory to provide a better understanding of the T-P superposition principle. The intermer potential is separated into the repulsive reference and the attractive perturbed parts. The hard sphere potential is taken as the repulsive reference. The attractive part of the Mie (p, 6) potential is taken as the perturbation. The free energy for the reference system of hard chains is obtained from the integration of the hard chain equation of state from the Baxter-Chiew theory. The limiting case of the reference free energy at infinite dilution is derived from the direct evaluation of the configurational partition function. The average packing energy is added as a perturbation energy. The local packing in the nearest neighbor is taken into consideration by the packing energy. The formulated free energy gives a unique interpretation of the empirical T-P superposition principle. The shape of the free energy is shown to be dominantly determined by the packing energy, especially by its (Mie potential) exponents. Therefore, its shape is dominantly temperature insensitive, which is the essence of the T-P superposition principle. In addition, it is shown that the theoretical internal pressure evaluated at atmospheric pressure possesses a maximum at a moderate temperature. At this point, the repulsion in the system starts to dominate the attractive interaction. Some experimental support for this behavior was given in the recent investigations into the bulk data of various polymers. These two features of the model yield the excellent correlation between the experimental and the theoretical polymer bulk properties. Better performance in fitting volumetric data is obtained if a more repulsive potential (p > 12) than the Lennard-Jones potential (p = 12) is used as a choice of the general Mie potential. This procedure culminates in the prediction of the cohesive energy (CE) of linear polyethylene at room temperature. The model with the Mie (18,6) potential gives the calculated CE within the experimental range, whereas the model with the Lennard-Jones potential overestimates the CE.