Experimental heat capacity, Cp,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 Cp,app of glass. Increase in the aging time, tage, or aging temperature, Tage, interferes with the onset temperature of Cp,app increase toward the liquid state value. When the endothermic feature is not obvious in the Cp,app-T plots of the glassy state, its presence may be discerned in a plot of dCp,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 Cp,app data to examine how much our violation of the Clausius theorem affects the entropy determined from the Cp,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 δCp,app d ln T integrals (δCp,app is the difference between the Cp,app of the aged and the unaged glass) measured only on the heating paths. The closed cycle Cp,app d ln T integral value is negligibly small. The δCp,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 Cp,app d ln T integral of an aged glass.