The equilibrium heat capacity C-p of a liquid whose molecules polymerized to form a linear chain structure at a fixed temperature has been measured at a fixed frequency of 3.33 mHz in real time simultaneously with the extent of polymerization alpha. The polymerization temperatures and this frequency were chosen such that the fully polymerized state remained a liquid and no heat capacity relaxation occurred. The plots of C-p against alpha show a maximum. This confirms the recent theoretical conclusions based on the polymer chain statistics [J. Wang and G. P. Johari, J. Chem. Phys. 116, 2310 (2002)] that during the course of a melt's polymerization, the configurational heat capacity of the equilibrium liquid reaches a maximum value at a certain alpha, and then decreases to the finite value of the fully polymerized melt. The results are also discussed in terms of the potential energy landscape at a fixed temperature where each new covalent bond formed and/or a new molecular weight distribution causes the state of the sample to enter a new landscape with a new set of potential energy minima of different depths and widths.