10 min readConcept sheetLab visit (observed): viva questions, a 5-mark note on Atwater factors and a calculation; can come as a 10-mark write-up

Calorific value by the bomb calorimeter (lab visit)

A dried food pellet is burnt in oxygen under pressure; the temperature rise × the calorimeter's heat capacity gives its gross energy.

MeasuresGross energy (heat of combustion), in kcal or kJ per g

StandardBenzoic acid, about 26.45 kJ/g (6.32 kcal/g)

Key formulaHeat released = heat capacity (kcal/°C) × temperature rise (°C)

Atwater factorsProtein 4, fat 9, carbohydrate 4 kcal/g (physiological)

Aim and principle

Lab visit: observed at a food analysis laboratory, not performed by you (but the write-up, viva and calculation are asked). Aim: To find the calorific value (gross energy) of a food sample with a bomb calorimeter. Principle: A weighed, dried sample is burnt completely in a sealed steel vessel (the bomb) filled with pure oxygen at about 25-30 atmospheres. The bomb sits in a known mass of water inside an insulated jacket, so all the heat of combustion passes into the bomb, bucket and water. The temperature rise is measured to 0.01 °C. Heat released = heat capacity of the calorimeter × temperature rise. The heat capacity is found first by burning benzoic acid, a standard whose heat of combustion is accurately known. Older books split the heat capacity into the mass of water plus the water equivalent of the bomb, bucket, stirrer and thermometer.

Requirements

Item	What it does
Bomb calorimeter: steel bomb, water bucket, stirrer, insulated jacket	Burns the sample in a closed space and holds the heat
Oxygen cylinder with pressure gauge	Fills the bomb with oxygen at about 25-30 atm for complete burning
Benzoic acid (thermochemical standard)	Known heat of combustion; used to find the heat capacity
Pellet press and crucible	Makes a firm pellet (about 1 g) that burns evenly
Fuse (ignition) wire and cotton thread	Ignites the pellet electrically
Sensitive thermometer (Beckmann or digital, 0.01 °C)	Measures the small temperature rise
Analytical balance; dried, ground food sample	Accurate weighing of standard and sample

Procedure

Observed at the laboratory. Typical quantities are given; follow the exact method in your lab manual.

1★
Standardise first: burn a weighed pellet of benzoic acid (about 1 g) by steps 2-7 to find the heat capacity.
2
Dry and grind the food; press about 1 g into a pellet and weigh it accurately in the crucible.
3
Fix the fuse wire between the electrodes so that it touches the pellet.
4
Close the bomb and fill it slowly with oxygen to about 25-30 atm.
5
Place the bomb in the bucket with a known mass of water (e.g. 2000 g); connect the firing leads, close the jacket and start the stirrer.
6★
Record the temperature every minute until it is steady; fire the sample and keep recording until the temperature peaks and starts to fall slowly.
the rise is usually 1-3 °C
7
Release the pressure slowly, open the bomb and check that burning was complete (no soot or unburnt sample).

★ one-way, controls the pace

Worked example 1: heat capacity and gross energy

Problem

Standardisation: 1.000 g of benzoic acid (6.32 kcal/g) raised the temperature by 2.50 °C; the bucket held 2000 g of water. Test: 1.000 g of a dried cereal sample raised the temperature by 1.74 °C. Find the heat capacity, the water equivalent of the apparatus and the gross energy of the sample.

Working

Heat from benzoic acid = 1.000 g × 6.32 kcal/g = 6.32 kcal.
Heat capacity of the calorimeter = 6.32 kcal ÷ 2.50 °C = 2.528 kcal/°C (2528 cal/°C).
The water itself takes 2000 g × 1 cal/g/°C = 2000 cal/°C, so the water equivalent of the bomb, bucket, stirrer and thermometer = 2528 − 2000 = 528 g.
Heat from the sample = 2.528 kcal/°C × 1.74 °C = 4.399 kcal.
Gross energy = 4.399 kcal ÷ 1.000 g = 4.40 kcal/g, i.e. 440 kcal per 100 g of dry sample.
In SI units: 4.399 × 4.184 = 18.4 kJ/g.
Small corrections for the fuse wire, the acids formed in the bomb and heat lost to the surroundings (cooling correction) are left out here.

Answer

Heat capacity = 2.528 kcal/°C (water equivalent of the apparatus 528 g). Gross energy of the sample = 4.40 kcal/g (about 18.4 kJ/g), i.e. 440 kcal per 100 g dry matter.

From bomb values to Atwater's 4-9-4

Nutrient	Heat of combustion in the bomb (kcal/g)	Digestibility	Other loss	Physiological fuel value (kcal/g)
Carbohydrate	4.1	About 98%	None	4.1 × 0.98 ≈ 4
Fat	9.45	About 95%	None	9.45 × 0.95 ≈ 9
Protein	5.65	About 92%	About 1.25 kcal/g lost in urine as urea and other nitrogen compounds	(5.65 − 1.25) × 0.92 ≈ 4

Why the two values differ

In the bomb, food burns completely: carbon to CO₂, hydrogen to water and nitrogen to its oxides, and even dietary fibre burns. In the body, (1) digestion and absorption are not complete, so some energy is lost in faeces, and (2) protein is not fully oxidised: its nitrogen leaves in urine as urea, which still holds energy. Atwater corrected the gross values for both losses and rounded them to the 4-9-4 factors used on food labels and in diet calculations. (Atwater's own averages were slightly different: fat 9.40 kcal/g, and carbohydrate 4.15 kcal/g with 97% digestibility; both versions round to 4-9-4.)

Worked example 2: physiological energy with Atwater factors

Problem

A food contains 12 g protein, 2 g fat and 70 g carbohydrate per 100 g. Find its physiological energy value and compare it with its gross energy from the heats of combustion.

Working

Physiological energy = (4 × protein) + (9 × fat) + (4 × carbohydrate).
= (4 × 12) + (9 × 2) + (4 × 70) = 48 + 18 + 280 = 346 kcal per 100 g.
Gross energy = (5.65 × 12) + (9.45 × 2) + (4.1 × 70) = 67.8 + 18.9 + 287.0 = 373.7 kcal per 100 g.
Difference = 373.7 − 346 = 27.7 kcal, about 7% of the gross value, lost through incomplete digestion and urinary nitrogen.
In kJ: 346 × 4.184 = 1447.7, about 1448 kJ per 100 g.

Answer

346 kcal (about 1448 kJ) per 100 g is available to the body, against 373.7 kcal gross. Food labels use the physiological (Atwater) value.

Precautions and result

Fill oxygen slowly and never above the maker's recommended filling pressure (about 30 atm); keep oil and grease away from oxygen fittings.
Use a dry, firmly pressed pellet of about 1 g so it burns completely; check for soot after firing.
Stand clear when firing and release the pressure slowly before opening; wear goggles.
Use the same mass of water and the same conditions for the standard and the sample.
Result: The gross energy (calorific value) of the given food sample is ___ kcal/g (___ kJ/g).

Nutrition link

Bomb calorimetry is the basis of the energy values in food composition tables and on nutrition labels: Atwater's 4-9-4 factors came from bomb values corrected for digestibility and urinary losses. Dietitians use these factors to work out the energy of diets, recipes and therapeutic meals, and energy-balance studies burn faeces and urine in the bomb to find how much food energy the body actually kept.

Exam angle

Short answer: “What is the water equivalent of a bomb calorimeter?” The mass of water that would take up the same heat per °C as the bomb, bucket, stirrer and thermometer. It is found by burning benzoic acid, whose heat of combustion is known.

Short answer: “Why is benzoic acid used to standardise the bomb calorimeter?” It is pure, stable and not hygroscopic, burns completely and has an accurately known heat of combustion (about 26.45 kJ/g, or 6.32 kcal/g).

Structured question: “Why do physiological fuel values differ from bomb calorimeter values?” The bomb gives gross energy by complete burning (protein 5.65, fat 9.45, carbohydrate 4.1 kcal/g). In the body digestion is incomplete (about 92%, 95%, 98%) and protein loses about 1.25 kcal/g as urea in urine. Corrected and rounded: 4, 9, 4 kcal/g (Atwater). Add a worked example.

Remember it

The bomb burns all, the body burns less: 5.65 / 9.45 / 4.1 in the bomb becomes 4 / 9 / 4 in the body.