Formulas

Body Mass Index p. 43

BMI = body mass ÷ (height)²

• body mass in kg
• height in m
• BMI in kg m⁻²

Nucleon number p. 175

nucleon number = number of protons + number of neutrons

Speed p. 228

speed = distance ÷ time

• speed in m s⁻¹
• distance in m
• time in s

Average speed p. 228

average speed = total distance ÷ total time

Velocity p. 229

velocity = displacement ÷ time

• velocity in m s⁻¹
• displacement in m

Acceleration p. 230

a = (v − u) ÷ t

• a = acceleration in m s⁻²
• v = final velocity
• u = initial velocity
• t = time taken

Energy units p. 50

1 kcal = 4200 J = 4.2 kJ

• 1 calorie (cal) = 4.2 joules (J)

Calorific value of food p. 52

Calorific value (kJ g⁻¹) = (4.2 J g⁻¹ °C⁻¹ × mass of water × change in water temperature) ÷ (mass of food sample × 1000)

• mass in g
• temperature change in °C

Carbon dioxide from electricity use p. 93

CO₂ released (g) = electrical energy used (kWh) ÷ 50 kWh × 39 g

• assumes 50 kWh of electrical energy produces 39 g of carbon dioxide

Rate of reaction p. 118

rate of reaction = change in the quantity of reactant or product ÷ time taken for the change to occur

• for example g s⁻¹ or cm³ s⁻¹

Rate at a specific time p. 121

rate of reaction at time t = gradient of the tangent to the curve at time t

General formula of alkanes p. 148

CₙH₂ₙ₊₂

• n = number of carbon atoms, 1, 2, 3, …

General formula of alkenes p. 148

CₙH₂ₙ

• n = number of carbon atoms, 2, 3, …

Fermentation p. 151

glucose → ethanol + carbon dioxide

• the zymase in yeast converts glucose

Soap production p. 167

oil + alkali → fatty acid salt (soap) + glycerol

• alkali = concentrated sodium hydroxide or concentrated potassium hydroxide

Ions in sodium chloride p. 179

NaCl → Na⁺ + Cl⁻

• Na⁺ = sodium ion (positively charged)
• Cl⁻ = chloride ion (negatively charged)

Magnifying power of microscope p. 211

magnifying power of microscope = magnifying power of objective lens × magnifying power of eyepiece

• example: 40 × 4 = 160 times

Telescope in normal adjustment p. 212

distance between objective lens and eyepiece = fₒ + fₑ

• fₒ = focal length of objective lens
• fₑ = focal length of eyepiece

Hydraulic system p. 224

input force ÷ area of small piston = output force ÷ area of large piston

• pressure at small piston = pressure at large piston
• example: 10 N on 2 cm² gives 500 N on 100 cm²

Period of orbit p. 241

T = length of orbit ÷ speed of satellite = 2π × (orbital height + radius of Earth) ÷ speed of satellite

• T = period of orbit
• radius of Earth = 6.37 × 10⁶ m

Orbits in a day p. 241

frequency of the ISS orbiting Earth in a day = 86400 s (1 day) ÷ period of orbit, T

• 86400 s = 1 day