Review for Exam #3. Refrigeration. Refrigerants/Coolants

Transcription

1 Review for Exam #3 Refrigeration 2 Refrigerants/Coolants Cold water (at say, 0 C) Heat extracted from product is used as sensible heat and increases water temperature Ice (at 0 C) Heat extracted from product is used as latent heat and melts ice ( fusion = kj/kg at 1 atm, 0 C); it can then additionally extract heat from product and use it as sensible heat to increase the temperature of water Dry ice (Solid CO 2 ) Heat extracted from product is used as latent heat and sublimates dry ice ( sublimation = 571 kj/kg at 1 atm, -785 C) Liquid nitrogen Heat extracted from product is used as latent heat and evaporates liquid N 2 ( vaporization = 199 kj/kg at 1 atm, C) Why does dry ice sublimate while regular ice melt under ambient conditions? 3 1

2 Phase Diagram Water CO 2 Solid Liquid Gas Solid Liquid Gas Pressure (atm) Melting point Triple point Boiling point Pressure (atm) 51 Triple point Temperature ( C) Temperature ( C) 4 Vapor Compression Refrigeration System Liquid Expansion Valve Liquid + Vapor P 2 P 1 d e Saturated Liquid Line SUB-COOLED LIQUID d High Pressure Side Low Pressure Side Evaporator Expansion Valve e Energy Output c Condenser Energy Input d e a Condenser Evaporator LIQUID + VAPOR H 1 Enthalpy (kj/kg) Critical Point ~ 30 C ~ -15 C Vapor Vapor b Compressor c Saturated Vapor Line b Compressor a a b SUPERHEATED VAPOR H 2 H 3 Energy Input Condensing: Constant Pr (P 2 ) Expansion: Constant Enthalpy (H 1 ) Evaporation: Constant Pr (P 1 ) Compression: Constant Entropy (S) Constant Temperature Line Left of dome: Vertical Within dome: Horizontal Right of dome: Curved down Ideal: Solid line Real/Non ideal: Dotted line (Super heating in evaporator, sub cooling in condenser) 5 Pressure-Enthalpy Diagram for R-12 Lines of Constant Values for Various Parameters Absolute Pressure (bar) Sub Cooled Liquid Liquid Vapor Mixture Superheated Vapor Const Pressure Const Enthalpy Const Temp Const Entropy Const Dryness Fraction Specific Enthalpy (kj/kg) 6 2

3 Pressure-Enthalpy Table for R-12 P H Diagram for Ideal Conditions e H 1 = h f based on temperature at d (exit of condenser) H 2 = h g based on temperature at a (exit of evaporator) Note 1: If there is super heating in the evaporator, H 2 can not be obtained from P H table Note 2: If there is sub cooling in the condenser, H 1 can not be obtained from P H table Note 3: For ideal or non ideal conditions, H 3 can not be obtained from P H table (For the above 3 conditions, use the P H Diagram to determine the enthalpy value) 7 Pressure-Enthalpy Diagram for R-12 Degree of sub cooling Real/Non Ideal Conditions Conditions (Determination of Enthalpies) Absolute Pressure (bar) Condenser Pressure Animated Slide Condensation Expansion Compression (See next slide Evaporation for static version of slide) Evaporator Pressure Q e = m (H 2 H 1 ) Q w = m (H 3 H 2 ) Degree of super heating Q c = m (H 3 H 1 ) Note: Q c = Q e + Q w H 1 H 2 H 3 COP = Q e /Q w = (H 2 H 1 )/(H 3 H 2 ) Specific Enthalpy (kj/kg) 8 Pressure-Enthalpy Diagram for R-12 Degree of sub cooling Real/Non Ideal Conditions Conditions Absolute Pressure (bar) Expansion Condenser Pressure Condensation Compression Evaporation Evaporator Pressure Q e = m (H 2 H 1 ) Q w = m (H 3 H 2 ) Degree of super heating Q c = m (H 3 H 1 ) Note: Q c = Q e + Q w H 1 H 2 H 3 COP = Q e /Q w = (H 2 H 1 )/(H 3 H 2 ) Specific Enthalpy (kj/kg) 9 3

4 Processes undergone by Refrigerant Evaporation Constant pressure process Liquid + Vapor => Vapor Compression Constant entropy process Vapor => Vapor Condensation Constant pressure process Vapor => Liquid Expansion Constant enthalpy process (adiabatic process; Q transfer = 0) Liquid => Liquid + Vapor 10 Cooling Load Rate (Q e ) Useful cooling effect takes place in evaporator Units of Q e : kw or tons 1 ton refrigerant = Power required to melt 1 ton (2000 lbs) of ice in 1 day = (2000* kg) (33494 x 10 3 J/kg) / (24 x 60 x 60 s) (2000 lb/ton)*( kg/lb) = Watts fusion (ice) (24 hr/day)*(60 min/hr)*(60 s/min) 11 Water Cooled Condenser A water cooled condenser is a double tube heat exchanger (co- or counter-current) with the refrigerant in the inside tube and cold water in the outer annulus It is used when Temperature of refrigerant in condenser is not much higher than the ambient air temperature (In this case, refrigerant can not lose much energy to outside air) OR Additional cooling of refrigerant is desired (beyond cooling capacity of ambient air) Q condenser ) m refrigerant (H3 H 1) m cold watercp(cold water) (Tcold(out ) Tcold(in ) 12 4

5 Heat Transfer in Refrigeration Applications What should be the rating of a room AC unit to maintain room at 20 C when it is 45 C outside? Q e = T/[(x 1 /k 1 A) + (x 2 /k 2 A)+(1/h i A i )+(1/(h o A o )+ ] 45 C 20 C What should be the rating of a refrigeration system to cool a product from 70 C to 20 C when it is flowing at a certain rate in a double tube heat exchanger? m (H H ) m c (T T ) Q e refrigerant 2 1 product p(product) product (in) product(out) 70 C 20 C OR Q e = U A lm T lm with 1/(UA lm ) = 1/(h i A i ) + r/(ka lm ) + 1/(h o A o ) How long will it take to cool an object of mass m from an initial temperature of T i to a final temperature of T f? Q e = {m c p (T)}/{Time} with T = T i T f 13 Summary: Vapor Compression Refrig System Liquid Expansion Valve Liquid + Vapor Condenser High Pressure Side Low Pressure Side Evaporator Ideal: Solid line Q e Real/Non ideal: Dotted line (Sup heat in evap, sub cool in cond) d e SUB-COOLED LIQUID Q c LIQUID + VAPOR a Critical Point Saturated Liquid Line Degree of sub cooling d d Condenser P 2 ~ 30 C Expansion Valve ~ -15 C P 1 e e Evaporator c Condensing: Constant Pr (P 2 ) Vapor Expansion: Constant Enthalpy (H 1 ) Evaporation: Constant Pr (P 1 ) b Compression: Constant Entropy (S) Compressor Q e = m (H 2 H 1 ) Q w Q w = m (H 3 H 2 ) Q c = m (H 3 H 1 ) Vapor Note: Q c = Q e + Q w From P H Table (For Ideal Conditions) H 1 = h f based on temp at d (exit of cond) H 2 = h g based on temp at a (exit of evap) Saturated Vapor Line COP = Q e /Q w = (H 2 H 1 )/(H 3 H 2 ) c b b Q e : Cooling load rate (kw) Q w : Work done by compressor (kw) Compressor COP: Coefficient of performance a a SUPERHEATED VAPOR Degree of superheating H 1 Enthalpy (kj/kg) H 2 H 3 14 Freezing 15 5

6 Freezing Purpose of freezing of foods To slow down rates of detrimental reactions by lowering temperature and water activity (a w ) Microbial spoilage Enzyme activity Nutrient loss Sensorial changes Prolongs shelf life beyond that of refrigerated foods Water activity (a w ): Amount of water available for reactions; a w = equilibrium relative humidity Guideline: Generally, rates of reactions double for every 10 C rise in temperature 16 Freezing of Foods Quality of frozen food depends on Rate of freezing ( C/hr) Ambient storage (freezing medium) temperature (T ) Constancy of temperature (cycling of temp is not good) Factors affecting rate of freezing ( C/hr) Convective heat transfer coefficient (h) Ambient storage (freezing medium) temperature (T ) Advantages of rapid freezing Smaller ice crystals are formed Thus, less structural damage to product Prevents concentration (of sugars, fats etc) Freezing time Time taken to freeze majority (~95%) of product A product is never completely frozen (~5-10% unfrozen) 17 Shelf Life High Quality Life (HQL) Period of frozen storage when a difference in quality can just be detected Practical storage life (PSL) Period of frozen storage during which product retains its characteristics and is suitable for consumption At -12 C PSL = ~ 4 months for fruits and seafood PSL = ~ 6 months for vegetables PSL = ~ 8 months for meats Typical frozen storage temperature Fruits and vegetables: ~ -18 C Ice cream and fatty fish: ~ -25 C 18 6

7 Freezer Burn Refers to moisture loss as ice crystals sublimate from surface Produces brownish spot as tissue becomes dry Could cause off-flavors It is a quality issue and not a safety issue Moisture resistant wrap can prevent freezer burn 19 Freezing Curve Sensible Heat Removal Latent Heat Removal Sensible Heat Removal Initial Freezing Point (T F ) 20 Types of Freezers Direct contact (usually, Individual Quick Freeze -- IQF type) Air blast Fluidized bed (particles on mesh conveyor; air from below) Immersion (N 2, CO 2, Freon) Fastest, but most expensive Indirect contact Plate (usually, food is within package) Apply pressure on plates to minimize resistance to heat transfer Air blast (usually, food is within package) Scraped surface heat exchanger Jacket (evaporator) has refrigerant 60-80% of latent heat is removed Product exits as a slurry Freezers can be batch or continuous 21 7

8 Freezing Medium Ice (Melting) At atmospheric pressure, melting point is 0 C Latent heat of fusion ( fus ) = 6,003 J/mol = 3335 kj/kg Liquid nitrogen (Evaporation) At atmospheric pressure, boiling point is C Latent heat of vaporization ( vap ) = 5,580 J/mol = 199 kj/kg Dry ice -- solid CO 2 (Sublimation) At atmospheric pressure, sublimation point is -785 C Latent heat of sublimation ( sub ) = 25,214 J/mol = 571 kj/kg 22 Depression in Freezing Point (T f ) Addition of a solute (say, salt) in a solvent (say, water) decreases freezing point from T to T, with T being determined by the Clausius-Clapeyron equation: fusion(water) 1 1 ln(x w ) R g T T' X w : Mole fraction of water fusion (water) : Latent heat of fusion of solvent (water) fusion (water) at atmospheric pressure = 6,003 J/mol = 3335 kj/kg R g : Universal gas constant = 8314 J/mol K T: Freezing point of pure solvent (water) in Kelvin; T = 273 K T : Freezing point of solution after adding solids (in Kelvin) T f : Depression in freezing point (= T T ) 23 Freezing Time (t f ): Plank s Equation f t f T T fusion (product) F P'a h R'a k f : Density of frozen product, kg/m 3 k f : Thermal conductivity of frozen product, W/m K fusion (product) : Latent heat of fusion of product, J/kg fusion (product) ~ (% moisture) x ( fusion (water) ) T F : Initial freezing point of product, K T : Temperature of freezing medium, K h: Convective heat transfer coefficient, W/m 2 K f 2 Sphere: a = diameter, P = 1/6, R = 1/24 Infinite cylinder: a = diameter, P = 1/4, R = 1/16 Infinite slab: a = thickness, P = 1/2, R = 1/8 24 8

9 Plank s Equation (Assumptions) At t = 0, the product is at its initial freezing point Time for removal of latent heat is determined Time for removal of sensible heat is not accounted for This can be calculated using Heisler chart Freezing takes place in 1 dimension (direction) only Applies to: Sphere, infinite cylinder, infinite slab Density and thermal conductivity of the product remain constant during freezing 25 Evaporation 26 Vapor Pressure Consider a liquid in a beaker at atmospheric pressure The molecules at the surface are bound by only the molecules below it All other layers have binding forces from the layers above and below it Thus, some molecules (having higher kinetic energy), leave the bulk of the liquid in vapor form and exert a pressure back on the liquid surface This is the vapor pressure of the liquid at that temperature Vapor pressure increases non-linearly with temperature Volatile liquids have a high vapor pressure at ambient temperature 27 9

10 Boiling Point (BP) Boiling point is the temperature at which vapor pressure of liquid equals surrounding pressure Boiling point of water at sea level at atmospheric pressure is 100 C Boiling point in Denver is ~94 C Boiling point at top of Mt Everest is ~71 C Boiling point decreases ~1 C for every 285 ft elevation 28 Elevation in Boiling Point When a solute is added to pure water, the boiling point of the resulting solution rises from T to T and is determined using the following equation: X ln(xw ) R vap g 1 1 T' T m / M with w w w mw / M w ms / Ms m = Mass of solute or water M = Molecular weight of solute or water X w = Mole fraction of water in the solution T = Boiling point of pure water (in Kelvin) = 373 K T' = Boiling point of solution after addition of solids (in Kelvin) R g = Universal gas constant = 8314 J/mol K λ vap = Latent heat of vaporization of water (λ vap of water at atm pr = 2,25706 kj/kg = 40,62708 J/mol) T b = Elevation in boiling point = T - T Subscripts: s for solute and w for water 29 What happens during Evaporation? Boiling point of solution rises Due to increase in solids content T between steam and product decreases Due to steam temperature remaining constant and product temperature (boiling temperature) increasing Rate of heat transfer decreases Due to T between steam and product decreasing 30 10

11 Types of Evaporators Batch-type pan Natural circulation Rising-film Falling-film Rising-falling-film Forced circulation Agitated (or mechanical) thin-film 31 Types of Evaporators (contd) Rising Film Falling Film Falling Film 32 Capacity and Steam Economy Capacity (m v ) Amount of water vaporized per unit time (kg/hr) Steam Economy (SE) Ratio of mass of water vapor produced to mass of steam used m SE m v s ~ 10 for a sin gle effect evaporator 33 11

12 Multiple Effect Evaporator (Different Arrangements) Forward Feed Backward Feed Parallel Feed 34 Thermal Recompression (Forced Circulation) 1 Steam jet 2 Venturi tube 3 Circulation pump F Feed P Concentrated product S Steam C Condensate V Vapor V 1 Vapor that is not recompressed (goes to condenser or another stage) 35 Mechanical Recompression (Natural Circulation) 36 12

13 Design of an Evaporation System For each effect, determine steam requirement (m s ) by performing Mass balance Solids balance Energy balance Use Q = UA(ΔT) to determine area required for heat transfer 37 Psychrometrics 38 Psychrometric Chart: 6 Quantities Dry bulb temperature, T db ( C) Temperature recorded by a regular thermometer Wet bulb temperature, T wb ( C) Temp of a thermometer with air blowing over a moist wick on its bulb Moisture content or specific humidity, W (kg water / kg dry air) Amount of moisture in air (also called, absolute humidity) Relative humidity (RH), (%) Ratio of amount of moisture in air to max amt of moisture air can hold Specific volume, V (m 3 /kg dry air) Volume of moist air per unit mass of dry air (specific volume = 1/density) Enthalpy, H (kj/kg dry air) Energy content of air Note 1: Each psychrometric chart is created at some constant pressure (most are for atmospheric pressure) So, psychrometric charts can not be used to analyze processes in which the pressure changes Note 2: Human comfort zone is at ~70-80 F & ~40-60% RH 39 13

14 Measurement of Wet Bulb Temperature Place a moist wick over the bulb of a mercury thermometer Blow air at high speed over the wick High energy water molecules from the wick evaporates since vapor pressure of water vapor near the wick is higher than that of the bulk surrounding air Latent heat for evaporation (of high energy water molecules) is removed from the wick, causing a decrease in temperature As the temperature of the wick decreases, sensible heat from air flows to it Equilibrium is attained when latent heat lost from the wick equals sensible heat flowing into the wick Note 1: If the relative humidity of the surrounding air is 100%, moisture will NOT evaporate from the wick and hence the reading of the wet bulb & dry bulb thermometers will the same Note 2: Greater the difference between T db & T wb, lower the RH of the surrounding air Note 3: This evaporative cooling principle provides cooling of water in an earthen pot 40 Dew Point Temperature (T dp ) It is the temperature at which moisture in a mixture of water vapor and air begins to condense (or form dew ) when cooled Q: Why does a soda can sweat? Q: When and why do we see our breath? 41 Lines of Constant Psychrometric Parameters Sensible heat factor Dry bulb Temperature ( C) Specific Volume (m 3 /kg dry air) Moisture Content (g/kg dry air) 42 14

15 Dew Point Temperature Dew point temp of air at A is determined by moving horizontally to the left and intersecting the 100% RH line (saturation temp line) & reading the temp at that point Note: T db = T wb at this point < * A Sensible heat factor Moisture Content (g/kg dry air) 43 Mixing Two Streams of Air A: m a kg/s B: m b kg/s C: Conditions of mixture L A to C : [m b /(m a + m b )]*L A to B L B to C : [m a /(m a + m b )]*L A to B Dry bulb Temperature ( C) A * C * Specific Volume (m 3 /kg dry air) B * Example: L A to B = 10 cm m a = 6 kg/s, m b = 2 kg/s Then, L A to C = [2/(2+6)]*10 = 25 cm L B to C = [6/(2+6)]*10 = 75 cm Moisture Content (g/kg dry air) Sensible heat factor 44 Air + Tiny Particles of Product Cyclone Separator Dry Product Spray Dryer Wet Product Atomizer Moist Product (Atomized) C Heater Hot Dry Air B Warm Moist Air + Dry Product Blower Ambient air A Atomization involves breaking up a liquid product into tiny droplets by forcing the product & compressed air into an atomizer (disc with multiple slots at periphery that spins at a high rpm) at the TOP This increases the surface area of the product, thereby increasing the rate of heat transfer, and thus the rate of evaporation In this lab, we are using a nozzle at the CENTER instead of a true atomizer at the TOP Spray dryer calculations involve: 1 Energy balance equation for air between points A & B (heater adds energy to air at point A ) 2 Water balance equation for air between points B & C (product adds moisture to air at point B ) 45 15

16 Heating of Air (Constant Moisture Content or Humidity Ratio) Q: Why do we feel dry in a heated room? V Note : ma V' * > A B Energy Balance: m (H ) Q m (H ) Dry bulb Temperature ( C) a A * a B Moisture Content (g/kg dry air) Sensible heat factor 46 Drying of Product (Constant Enthalpy & Wet Bulb Temp) Adiabatic Process (Q = 0) If Q = 0 & work done = 0, then, H = Constant Part of sensible heat of air is converted to latent heat of water vapor; thus, temp drops; mc inc Water Balance: a B Dry bulb Temperature ( C) * C * m (W ) m (%moisture) m (W ) p B a C Moisture Content (g/kg dry air) Sensible heat factor 47 Heating Ambient Air & Drying a Product A: Ambient air B: Heated air C: Exit air (after heating product) Dry bulb Temperature ( C) C * * > * A Energy Balance B Moisture Content (g/kg dry air) Sensible heat factor 48 16

17 Thermal Processing (For Bonus Points) 49 Classification of Foods based on ph Low acid: ph 46; Acid: ph < 46 (C botulinum) More specific classification Low acid: ph > 53 Red meat, poultry, seafood, milk, corn, peas, lima beans, potatoes, cauliflower Medium acid: 45 < ph < 53 Spaghetti, soups, sauces, asparagus, beets, pumpkin, spinach, green beans, turnip, cabbage Acid: 37 < ph < 45 Tomato, pear, fig, pineapple, apricot, yogurt, white cheese, beer High acid: ph < 37 Sauerkraut, pickles, berries, citrus, rhubarb, wine, vinegar, plums, currants, apples, strawberries, peaches 50 Classification of Foods Based on mc or a w High moisture foods (50+% %) Fruits, vegetables, juices, raw meat, fish Intermediate moisture foods (15-50%) Bread, hard cheeses, sausages Low moisture foods (0-15%) Dehydrated vegetables, grains, milk powder, dry soup mixes Importance of a w : Honey at 20% mc is shelf stable, while potato at 20% is not 51 17

18 Classification of Bacteria Based on Oxygen Aerobes (Need oxygen for growth) Microaerophile: Need only small amount of oxygen for growth Anaerobes Obligate: Oxygen prevents growth Facultative: Can tolerate some degree of oxygen Based on temperature Psychrophiles (Grow best from F; grow slowly at refrigerator temp) Mesophiles (Grow best from F -- warehouse temps) Thermophiles (Optimum: F; spores can survive 250 F for 1+ hr) Based on salt, acid, water activity (a w ), osmotic pressure Halophiles (Can not grow in absence of salt) Acidophiles (Can grow in high acid conditions even at ph of 20) Xerophiles (Can grow in low a w conditions) Osmophiles (Can grow in high osmotic pr conditions high sugar foods) Resistance of viruses > spores of bacteria > vegetative cells of bacteria > molds and yeasts Target organism & surrogate need to be identified for each product process combination 52 Blanching Mild heat treatment (~90 C) for few minutes Heating medium Water or steam Purposes Inactivate enzymes Reduce microbial load Wilt vegetables for efficient packing into cans 53 Pasteurization All vegetative pathogenic organisms inactivated (not spores) Public health significance (earlier target: Mycobacterium tuberculosis) Some spoilage organisms may survive HTST (Targets veg state of Coxiella burnetti => Q fever) Spoilage organisms that can grow at room temp are destroyed 15 s at 161 F (~72 C) Equivalent batch (Vat): 30 min at 145 F (~63 C) If milk product has > 10% fat, is condensed, or is sweetened, increase temperature by 3 C (or 5 F) For eggnog, use 155 F (~69 C) for 30 mins, 175 F (~80 C) for 25 s, or 180 F (~83 C) for 15 s Shelf life: ~ 3 weeks HHST (191 F for 10 s to 212 F for 001 s) Coxiella burnetti: Obligate intracellular bacterium; cat B bioterrorism agent (z = 44 C) Other concerns: Salmonellosis, staphylococcal infection, and streptococcal infection 54 18

19 Extended Shelf Life (ESL) Shelf life is between that of pasteurized and UHT product (often minimally processed and refrigerated) Advantages: Longer distribution, cheaper than UHT If ESL process is to be closer to pasteurization Use filtration/centrifugation to remove spore-formers This may constitute 1-2% of product volume Sterilize this and mix with original product Products Lunch meats, cured meats, seafood, salads, fresh pasta, sauces, entrees Organisms of concern Mesophiles and psychrotrophs 55 Ultra-Pasteurization 280 F (~138 C) for 2 s Vegetative organisms killed; not spores Product must be refrigerated Nearly sterile Filler may not meet aseptic standards Shelf life: ~3 months Longer shipping distances Products: Cream, specialty dairy products Becoming more popular for milk 56 Ultra High Temperature (UHT) UHT = Aseptic All pathogenic and spoilage organisms (including spores) are killed Thermophilic organisms may survive Commercially sterile product 284 F (140 C) for 4 s Shelf life: 1-2 years UHT milk processing covered under 21CFR108, 21CFR113, 21CFR

20 Aseptic Processing A continuous thermal process in which the product and container are sterilized separately and brought together in a sterile environment Components: Pump, deaerator, heat exchanger, hold tube, cooling unit, back pressure device, packaging unit Temperature: C ( F) 58 Hot Fill Fill processed product in unsterile container Acid or acidified product (sterilization) Shelf stable product Low acid product (pasteurization) Refrigerated product Hot product (~90 C or 194 F) sterilizes container Invert container for 05 to 3 min Sterilize neck area Cooling of product Air cool Water spray Bernerfoodscom 59 Log scale D & z values Log scale Constant Temperature No of microorganisms (N) N 0 Slope = 1/D T D value (seconds) Slope = 1/z Time (seconds) Temperature ( C) N N 0 10 t D T D T D ref 10 Tref T z 60 20

21 F 10 t 0 TTref z F Value For a constant temperature process, F 10 z dt 10 t TTref z t Conservative F value is based on Center temperature of can (for retorting) Center temp at holding tube exit (for aseptic process) Fastest flowing fluid element or particle i1 Ti Tref F 0 = F value when T ref = 250 F & z = 18 F (or T ref = 1211 C & z = 10 C) n i t: Process time 61 Microbiological Approach to Calculating F Value Log scale N0 F Dref log N Log scale No of microorganisms (N) N 0 Slope = 1/D Constant Temperature D value (seconds) Slope = 1/z Time (seconds) N N 0 10 t D T T Temperature ( C) D D ref 10 TTref z 62 Cook Value (C-Value) F t 0 10 TTref z dt C t 0 10 TTref zc dt Component z value ( C) Bacterial spores 7-12 Vegetative cells 4-8 Enzymes Vitamins Proteins Sensory attribute (Overall) Sensory attribute (Texture softening) Sensory attribute (Color) Source: Improving the thermal processing of foods (Richardson, 2004) Note: Generally, for canning & aseptic processing, T ref = 1211 C (or 250 F) Also, z c >> z in most cases 63 21

22 Time-Temperature Optimization Log scale Goal: Achieve required F 0 with a minimum C value Holding Time (seconds) Slope = 1/z Slope = 1/z c Temperature ( C) Note: Generally, z c >> z 64 Accelerated Shelf Life Testing (ASLT) Select at least 3 elevated temperatures 5+ C apart Determine shelf life at these temperatures Plot shelf life (log scale) on y-axis and temperature (on x-axis) Extrapolate graph to determine shelf life at desired temperature Shelf Life (Log Scale) * * * Temperature Other: Cycling temperature between 0 C and room temp; controlled shaking 65 TTI A biological/chemical/physical indicator that undergoes a precise, measurable, and irreversible change in some attribute that depends on the timetemperature combination it experienced Classification of TTIs Biological, chemical, physical Single or multiple response Intrinsic or extrinsic Dispersed, permeable or isolated Volume averaged or single point 66 22