Key Formulas & Equations
Relative Humidity: ERH = aw × 100%
Saturated Solution: aw = 1.0; Dry food: aw < 0.6
Microbial Growth Limit: Most bacteria: aw > 0.91; Yeasts: aw > 0.88; Molds: aw > 0.80
Thermal Death Time: F-value = t × 10((T-Tref)/z)
Z-value: Temperature change for 10× change in D-value
Sterilization (12D): F₀ = 12 × Dref
Moisture Content (dry basis): MCd = (Ww - Wd)/Wd × 100%
Water Sorption Isotherm: aw vs. MC relationship
titratable Acidity: TA = (V × N × equivalent weight) / sample weight
Brix (Sugar): °Bx = g sucrose / 100 g solution
Raoult's Law (aw): aw = xwater = nwater/(nwater + nsolute)
Glass Transition: Tg = temperature where rubbery → glassy
Shelf Life: Q₁₀ = rate at (T+10°C) / rate at T (typically 2-4)
Core Concepts
Food Chemistry
Study of chemical processes and interactions of food components: carbohydrates, proteins, lipids, water, vitamins, and minerals. Includes Maillard reaction, caramelization, and lipid oxidation.
Food Microbiology
Study of microorganisms in food: bacteria, yeasts, molds, and viruses. Includes foodborne pathogens (Salmonella, E. coli, Listeria) and beneficial microbes (fermentation).
Food Processing
Techniques to transform raw ingredients into food products: thermal processing, freezing, drying, fermentation, extrusion, and high-pressure processing.
Food Preservation
Methods to extend shelf life and prevent spoilage: canning, pasteurization, refrigeration, freezing, drying, irradiation, and chemical preservatives.
Food Safety & HACCP
Hazard Analysis Critical Control Points (HACCP) is a systematic approach to identify, evaluate, and control food safety hazards throughout the supply chain.
Food Rheology
Study of flow and deformation of food materials. Important for texture, mouthfeel, and processing. Includes viscosity, elasticity, and plasticity.
Food Packaging
Materials and technologies to protect food and extend shelf life. Includes active packaging, modified atmosphere packaging (MAP), and biodegradable packaging.
Nutrition & Functional Foods
Study of food components that provide health benefits beyond basic nutrition. Includes probiotics, prebiotics, antioxidants, and bioactive compounds.
Worked Examples
Example 1: Water Activity
Problem: A food product has vapor pressure of 2.3 kPa at 25°C. Pure water vapor pressure = 3.17 kPa. Calculate aw.
Solution:
aw = P/P₀ = 2.3/3.17 = 0.726
Interpretation: aw < 0.85, so most bacteria cannot grow
Example 2: Freezing Point Depression
Problem: A 10% NaCl solution (Kf = 1.86 °C/m). Calculate freezing point depression.
Solution:
m = 10 g/58.44 g/mol / 0.09 kg = 1.90 m
ΔTf = 1.86 × 1.90 = 3.54°C → Freezing point = -3.54°C
Example 3: Moisture Content
Problem: A food sample weighs 50 g fresh and 15 g after drying. Calculate moisture content (wet basis).
Solution:
MC = (50 - 15)/50 × 100% = 70%
Practice Problems
Problem 1
Calculate aw for a saturated NaCl solution (26.4% w/w). Assume Raoult's law.
Answer: aw ≈ 0.75 (known value for saturated NaCl)
Problem 2
Calculate D-value reduction time at 121°C if D₁₂₁ = 1.5 min and z = 10°C for 12D sterilization.
Answer: F₀ = 12 × 1.5 = 18 minutes
Problem 3
Calculate titratable acidity if 10 mL juice requires 8 mL of 0.1 N NaOH to reach pH 8.2.
Answer: TA = (8 × 0.1 × 0.064)/10 = 0.051 g citric acid/100 mL
Problem 4
Calculate Brix for a solution with 25 g sucrose in 100 g total solution.
Answer: °Bx = 25
Problem 5
Calculate moisture content (dry basis) for a product with 30% wet basis moisture.
Answer: MCd = 30/70 × 100% = 42.9%
Problem 6
Calculate Q₁₀ if spoilage rate doubles when temperature increases from 4°C to 14°C.
Answer: Q₁₀ = rate at 14°C / rate at 4°C = 2
Problem 7
Calculate freezing point depression for 5% sugar solution (Kf = 1.86 °C/m, MW = 342).
Answer: m = 5/342/0.095 = 0.153 m; ΔTf = 1.86 × 0.153 = 0.28°C