[...]... of unknown variables and the number of independent equations 10 In a properly specified problem of mass balance, the degrees of freedom must not be equal to zero Examples Example 3.1 How much dry sugar must be added in 100 kg of aqueous sugar solution in order to increase its concentration from 20% to 50%? S Yanniotis, Solving Problems in Food Engineering Ó Springer 2008 11 12 3 Mass Balance Solution... main reason steam is used as a heating medium is its high latent heat value 17 About 5.4 times more energy is needed to evaporate 1 kg of water at 100 8C than to heat 1 kg of water from 0 8C to 100 8C 18 The latent heat of vaporization becomes zero at the critical point 19 Superheated steam is preferred to saturated steam as a heating medium in the food industry S Yanniotis, Solving Problems in Food. .. atm (1 atm = 101325 Pa) Table 1.3 Conversion factors 1 ft = 12 in = 0.3048 m 1 in = 2.54 cm 1 US gallon = 3.7854 l 1 lbm = 0.4536 kg 1 lbf = 4.4482 N 1 psi = 6894.76 Pa 1 HP =745.7 W 1 Btu = 1055.06 J = 0.25216 kcal 1kWh = 3600 kJ S Yanniotis, Solving Problems in Food Engineering Ó Springer 2008 – Btu HP, PS ft2 ft3 lbm/ft3 ft/s psi=lbf /in2 0 F = 32þ1.8* 0C C = (0F-32)/1.8 0 R = 460 þ 0F K = 273.15... per unit mass of fluid in the system, J/kg t = time, s In most of the cases, the overall energy balance ends up as an enthalpy balance because the terms of kinetic and potential energy are negligible compared to the enthalpy term, the system is assumed adiabatic (Q ¼ 0), and there is no shaft work (Ws ¼ 0) Then: X _ mH ¼ 0 S Yanniotis, Solving Problems in Food Engineering Ó Springer 2008 21 22 4 Energy... respectively, find the enthalpy at 53 8C Solution Find the enthalpy at 53 8C by interpolation between the values for 50 8C and 558C given in steam tables, assuming that the enthalpy in this range changes linearly: H ¼ 2592:1 þ 53 À 50 ð2600:9 À 2592:1Þ ¼ 2597:4 kJ=kg 55 À 50 Exercises Exercise 2.1 Find the boiling temperature of a juice that is boiling at an absolute pressure of 31.19 Pa Assume that the boiling... temperature in the autoclave is lower than the saturation temperature at 232 kPa, the partial pressure of water vapor in the autoclave is less than 232 kPa Therefore air is present in the autoclave Exercise 2.6 Lettuce is being cooled by evaporative cooling in a vacuum cooler If the absolute pressure in the vacuum cooler is 934.9 Pa, determine the final temperature of the lettuce (Hint: Find the saturation... milk is heated to 1458C by introducing it into the steam infusion chamber H and then is cooled quickly by flashing in the flash vessel F The vapor that flashes off in the vessel F is condensed in the condenser C by direct contact of the vapor with cooling water To avoid dilution of the milk, the pressure in the vessel F must be such that the rate at which vapor flashes off in the vessel F is equal to... Energy Balance Review Questions Which of the following statements are true and which are false? 1 The energy in a system can be categorize as internal energy, potential energy, and kinetic energy 2 A fluid stream carries internal energy, potential energy, and kinetic energy 3 A fluid stream entering or exiting a control volume is doing PV work 4 The internal energy and the PV work of a stream of fluid... assumptions: l l l l The terms of kinetic and potential energy in the energy balance equation are negligible A pump is not included in the system (Ws ¼ 0) The heat capacity of the liquid streams does not change significantly with temperature The system is at steady state Step 3 Write the energy balance equation: _ Rate of energy input ¼ mw in  Hw in _ þ mm in  Hm in _ _ Rate of energy output ¼ mw... milk) At steady state rate of energy input ¼ rate of energy output or _ _ _ _ mw in  Hw in þ mm in  Hm in ¼ mw out  Hw out þ mm out  Hm out þ q Step 4 Calculate the known terms of eqn (4.1) i) The enthalpy of the water stream is: Input: Hw in Output: Hw ¼ cp T ¼ 4:2  90 ¼ 378 kJ=kg out ¼ cp T ¼ 4:2  75 ¼ 315 kJ=kg ii) The enthalpy of the milk stream is: Input: Hm in Output: Hm ¼ cp T ¼ 3:9  45 ¼ . class="bi x0 y0 w1 h1" alt="" Solving Problems in Food Engineering Stavros Yanniotis, Ph.D. Author Solving Problems in Food Engineering Stavros Yanniotis, Ph.D. Department of Food Science and Technology Agricultural. point. 19. Superheated steam is preferred to saturated steam as a heating medium in the food industry. S. Yanniotis, Solving Problems in Food Engineering. Ó Springer 2008 5 20. Steam in the food. evaporation, drying, thermal processing, cooling and freezing, etc. The most difficult part of a course in food engineering is often considered the solution of problems. This book is intended to