Experimental heat capacity, C-p,C-app, of some physically aged polymers had shown an endothermic peak or a shoulder on heating when the material was still in the glassy state. In the first part of this paper, we report observation of a similar feature in a molecular glass, sucrose, indicating increase in the enthalpy and entropy from kinetic unfreezing of molecular motions in the solid state. Aging decreases C-p,C-app of glass. Increase in the aging time, t(age), or aging temperature, T-age, interferes with the onset temperature of C-p,C-app increase toward the liquid state value. When the endothermic feature is not obvious in the C-p,C-app-T plots of the glassy state, its presence may be discerned in a plot of dC(p,app)/dT against T. Molecular motions producing this feature have implications for the state point in a potential energy landscape of an aging glass. In the second part of the paper, we use the C-p,C-app data to examine how much our violation of the Clausius theorem affects the entropy determined from the C-p,C-app d ln T integral. In addition to calculating this integral for a closed cycle of (irreversible) cooling and heating paths, we suggest an analysis which uses the delta C-p,C-app d ln T integrals (delta C-p,C-app is the difference between the C-p,C-app of the aged and the unaged glass) measured only on the heating paths. The closed cycle C-p,C-app d ln T integral value is negligibly small. The dC(p,app) d ln T integral value increases with tage. It is equal to the enthalpy lost on aging divided by Tage. Clausius theorem violation has no significant effect on determination of the entropy from C-p,(pp) d ln T integral of an aged glass.