Drying Tests with a Foodstuff. In order to test the feasibility of drying a certain foodstuff, drying data were obtained in a tray dryer with air flow over the top exposed surface having an area of 0.186 m². The bone-dry sample weight was 3.765 kg dry solid. At equilibrium after a long period, the wet sample weight was 3.955 kg H₂O + solid. Hence, 3.955 – 3.765, or 0.190, kg of equilibrium moisture was present. The following sample weights versus time were obtained in the drying test:

a. Calculate the free moisture content X kg H₂O/kg dry solid for each data point and plot X versus time. (Hint: For 0 h, 4.944 – 0.190 – 3.765 = 0.989 kg free moisture in 3.765 kg dry solid. Hence, X = 0.989/3.765.)

b. Measure the slopes, calculate the drying rates R in kg H₂O/h · m², and plot R versus X.

c. Using this drying-rate curve, predict the total time to dry the sample from X = 0.20 to X = 0.04. Use numerical integration for the falling-rate period. What are the drying rate R_C in the constant-rate period and X_C?