Question

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 sublimes, 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 Hg). The steaks, which contain 72% water by mass, enter the chamber at 26°C at a rate of 50 kg/min. 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 50°C.

(a) Use the heat capacity data given below and additional tabulated data for water to calculate the required heat input in kilowatts.

(Cp)ice =2.17 J/(g°C)

(Cp)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.

(c) Many substances, such as food and drugs, spoil if exposed too long to high temperatures (which accelerate rates of degradation) or to liquid water (which provides an environment for growth of microbial species that cause degradation). Also, rates of evaporation and sublimation increase as BIOENGINEERING Problems 477 WEBC08 06/04/2015 22:38:24 Page 478 temperature increases and pressure decreases. Use those observations to construct a oneparagraph explanation of how freeze-drying works and the reason for each step of the process. (For example, why is the sublimation done in a vacuum chamber?) Your explanation should be clear to someone with a nontechnical or nonscientific background.

Answer 1

a) Total Heat required = Heat required to rise Steak temperature from 26 to 50 C+Heat required to rise temperature of 96% water from 26 C to 60 C + Heat required to vaporise 96% water + Heat required to rise temperature of remaining water from 26 to 50 C

Heat required to rise Steak temperature from 26 to 50 C=Mass of Steak*Cp(Steak)*(50-26)

Per minute,

Total Inlet mass = 50 kg

Water content = 72%

=> Water mass = 72/100*50=36 Kg

=> Steak mass =50-36=14 kg

Heat required to rise Steak temperature from 26 to 50 C=14*1.38*(50-26)=463 KJ

Heat required to rise temperature of 96% water from 26 C to 60 C=96% of total water mass*Cp(Water)*(60-26)=96/100*36*2.17*(60-26)=2549 KJ

Latent heat of water =2200 KJ/kg

Heat required to vaporise 96% water=96% of total water mass*Latent heat = 96/100*36*2200=76032 KJ

Heat required to rise temperature of remaining water from 26 to 50 C= (1-96/100)*Total water mass*Cp(water)*(50-26)=(1-96/100)*36*2.17*(50-26)=75 KJ

=> Per minute, Total Heat required=463+2549+76032+75=79119 kJ

=> Power required = Heat in KJ/time(s) = 79119/60=1318 KW

b) Heat required only of phase change = Heat required to vaporise 96% water = 96/100*36*2200=76032 KJ

=> Error = (Total Heat required-Heat required only of phase change)/Total Heat required=(79119-76032)/79119=3.9%

c) Steps involved In dry freezing,

1) Substance is cooled down such that all water in the substance gets freezed

2) Vacuum is applied. Because of Vacuum, freezed water starts sublimating. It is because water phase is vapor on the reached pressure due to applied vacuum.

3) Hence substance lost water and got dehydrated. This is dry freezing because substance got dried (lost water) by freezing water