Bomb Calorimeter: Food Caloric Value Analysis

Sample

Macronutrient type

Sample mass 1.00 g

Water bath mass 2000 g

Live readouts

Load a sample and ignite to measure its caloric value.

Water ΔT

0.00 °C

Heat released

0 cal

Measured value

— kcal/g

Reference value

— kcal/g

How it works

A weighed food sample is sealed in a steel "bomb" with excess oxygen and submerged in a known mass of water. An electric wire ignites it; the sample burns completely and the heat released raises the water temperature. Because the whole system is a closed, constant-volume calorimeter, the heat released equals the heat absorbed by the water plus the calorimeter's own metal parts:

q_released = (m_water · c_water + C_bomb) · ΔT
c_water = 1.00 cal/(g·°C)     C_bomb ≈ 850 cal/°C (calibrated constant)
Caloric value (kcal/g) = q_released / (1000 · m_sample)

This is the gross (bomb-calorimetry) energy density — it burns the sample completely to CO₂ and H₂O, unlike the physiological Atwater factors used on nutrition labels, which subtract the energy lost to incomplete digestion and urinary nitrogen:

Macronutrient	Bomb value	Atwater (label) value
Carbohydrate	4.10 kcal/g	4 kcal/g
Protein	5.65 kcal/g	4 kcal/g
Fat	9.45 kcal/g	9 kcal/g

Sample mass — more sample releases more total heat but the calculated kcal/g should stay the same (it's an intensive property).
Water bath mass — a larger water bath absorbs the same heat with a smaller ΔT; the calculation compensates automatically.
Ignite — runs the combustion: sparks appear in the bomb, the water heats and its color shifts warm, the thermometer needle climbs to its plateau, and the readouts update live.

Real-world relevance: this exact technique (ASTM/ISO bomb calorimetry) is how the caloric values printed on food labels are originally derived in analytical nutrition labs.

Water temp.

25.00 °C

Oxygen bomb Water bath Ignition sparks

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