Entropy change on the cooling and heating paths between liquid and glass and the residual entropy

We analyze the C(p)-T data for the glassy state of eight materials of varied molecular interactions and structures to investigate how the use of the C(p)d ln T integral in the time-dependent (nonreversible) thermodynamic path between a liquid and glass affects our estimates of the entropy. Since the change in entropy on such a path cannot be determined, we estimate the upper and lower values of the change, Δσ, from the C(p)d ln T integral. For the same rates of cooling and heating and without annealing, Δσ on the cooling path is negligibly different from that on the heating path. The difference is ～1∕60th-1∕25th of the lowest known value of the residual entropy and even less than the configurational entropy of the supercooled liquid at its kinetic freezing temperature. Thus use of the C(p)d ln T integral in the nonreversible path does not introduce significant errors in estimating the residual entropy. Dynamic C(p) data cannot be used to infer that configurational entropy decreases on glass formation. Time dependence of the C(p)-T path has little consequence for reality of the residual entropy.