Freeze drying is a technique for dehydrating substances at low temperatures, thereby avoiding the degradation that may accompany heating. The material to be dried is cooled to a temperature at which all of the water present turns to ice. The frozen substance is then placed in a vacuum chamber and may also be subjected to radiant or microwave heating; the ice in the food sublimates, and the vapor is carried off by the vacuum pump. Steaks are to be freeze-dried in a heated chamber at 1 torr (1 mm He). The steaks, which contain 72% water by mass, enter the chamber at —26°C at a rate of 50 kg/mm. Of the water entering with the steaks, 96% leaves as a vapor at 60°C; the remainder leaves as a Liquid with the steaks at O°C.

(a) Use the heat capacity data given below and additional tabulated data for water to calculate the required heat input in kilowatts. (C_p) _ice = 2.17 J/ (g∙°C) (C_p) _{dry meat} = 1.38 J/ (g∙°C)

(b) When large temperature changes are not involved in a phase-change operation. a reasonable estimate of the required heat transfer rate may be obtained by neglecting contributions of temperature changes to the overall process enthalpy change (i.e.. by taking only phase changes into account). Moreover, it is often reasonable to use any available values of latent heats, neglecting their dependence on temperature and pressure. In the case of the freeze-drying process, the approximation might be to calculate only the heat needed to melt all the water and vaporize 96% of it, using latent heats at the normal melting and boiling points (Table B.1) and neglecting the heat required to raise the temperature of the meat and water. What percentage error in the calculated value of Q would result from this approximation? Take the value determined in part (a) to be exact.