Calculations for the Gibbs-Thomson effect and the intergranular melting of the ice droplets in (water) emulsions at temperatures below 273.16 K show that water and ice coexist at thermodynamic equilibrium in an apparently frozen emulsion. The fraction of water at this equilibrium increases on heating, which alters further the thermodynamic properties of the emulsion. As some of the ice in the emulsion has already melted, the increase in the enthalpy, H, and heat capacity, C-p, and the decrease in the volume measured on the normal melting at 273.16 K, are less than the values anticipated. The ratio of this increase in H, or C-p, on melting of the emulsion to the corresponding Value for pure ice, underestimates the emulsion's water content which, when used for scaling the difference between the C-p of the unfrozen and frozen emulsion at lower temperatures, as in earlier studies, leads to a larger C-p Of supercooled water than the actual value. Similar scaling of the corresponding difference between the volume leads to higher volume, or lower density, than the actual value. A formalism for this premelting effect is given for both the adiabatic and differential scanning calorimetry (DSC), and its magnitude is calculated. New experiments show that tile rise in the DSC signal, or equivalently in the apparent C-p observed on heating the frozen emulsion, occurs over a temperature range much wider than the Gibbs-Thomson effect and intergranular melting predict, for which reasons are given. It is shown that C-p of the dispersant phase is also affected by the melting of ice droplets. There are four consequences of the premelting effects for all finely dispersed materials, for frozen water emulsions below 273.16 K: (i) water and ice coexist in the emulsion, (ii) its apparent C-p will increase with increase in the heat input used to measure it, (iii) the apparent C-p will increase with decrease in the average size of the droplets, and (iv) the apparent C-p will decrease on annealing the frozen emulsion for a period long enough to allow the ice-grain growth in the frozen droplets. Calorimetry of emulsions has verified consequences (i) and (iv). The corresponding effects on the molar volume are briefly discussed. A substantial fraction of tile anomalously high C-p and volume of supercooled water is due to the observed premelting effects. (C) 1997 American Institute of Physics. [S002 1-9606(97)50147-4].