Heat of Combustion, per Fuel and per Oxygen

Choose a fuel and whether its water leaves as vapour, as from a flame, or as liquid, as in a calorimeter or your body. The page balances the combustion, then divides the same heat three ways: by the fuel's mass, by the oxygen's mass and by the oxygen's volume. The last two are the ones a fire laboratory and a hospital measure.

Worked example — Heat of Combustion, per Fuel and per Oxygen

Oxygen to burn one mole	2.00 mol
Heat released per mole	802.69 kJ/mol
Per kilogram of fuel	50.03 MJ/kg
Per kilogram of oxygen	12.54 MJ/kg
Per litre of oxygen, at 0 °C and 1 atm	17.91 kJ/L
Against Huggett's 13.1 MJ/kg	−4.25%
Heat from 1 kg of oxygen	12.54 MJ

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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Lesson

The theory — Heat of Combustion, per Fuel and per Oxygen

The heat of combustion is the enthalpy released when one mole of a fuel burns completely in oxygen: carbon to CO₂, hydrogen to H₂O, nitrogen to N₂. Measured in a bomb calorimeter the water condenses, and that figure is the higher heating value. Leave the water as vapour and each mole of it takes 44.004 kJ away, giving the lower heating value. The oxygen needed for C_cH_hO_oN_n is c + h/4 − o/2 moles, so the heat can be divided by the fuel's mass or by the oxygen's.

What each symbol means

ΔcH°: the standard enthalpy of combustion, in kJ per mole of fuel, at 25 °C with the water liquid. Negative, because heat leaves
n(O₂): moles of oxygen to burn one mole of fuel: c + h/4 − o/2
E: heat released per kilogram of oxygen consumed. Huggett's value, 13.1 MJ/kg, is what a fire laboratory assumes

Assumes: Complete combustion to CO₂ and H₂O at 25 °C and 1 bar, as in the NIST Chemistry WebBook's standard enthalpies. Where the WebBook lists a direct combustion measurement it is used as printed, and otherwise the heat is derived from a formation enthalpy: benzene, octane, acetylene, ammonia, hydrogen, carbon monoxide and graphite. The heat is defined with the products brought back to 25 °C; a flame's hot gases carry that same heat away until they cool. The litre of oxygen is at 0 °C and 1 atm, the physiologist's standard volume, treated as an ideal gas.
Breaks when: In a smoky fire, where part of the carbon leaves as CO rather than CO₂: carbon burned only to CO releases 221.06 kJ per mole of O₂ against 393.51 to CO₂, so each kilogram of oxygen releases less, and oxygen-consumption calorimetry has to measure the CO to correct for it. For fuels outside Thornton's class, as hydrogen and carbon monoxide show on this page. And in the body for protein, whose nitrogen leaves as urea rather than N₂, so neither the heat nor the oxygen follows the equation on this page.

Per kilogram of oxygen, fuels that differ 3.55-fold per kilogram come out within 5% of one number 🖖

Methane releases 50.03 MJ per kilogram and glucose 14.10, water as vapour in both. Divide by the oxygen each one uses and methane gives 12.54 MJ per kilogram of O₂ and glucose 13.24. On that basis eleven of the sixteen fuels here, gases, liquids, sugars, a fat and even ammonia, land within 5% of 13.1. Most of the heat is the energy of the C=O and O–H bonds each O₂ ends up in, and an O₂ molecule ends up in much the same bonds whatever it burns. William Thornton noticed it in 1917; Clayton Huggett at the US National Bureau of Standards fixed the number in 1980, 13.1 MJ/kg ± 5%. Fire laboratories use it, from the bench-top cone calorimeter to full-scale furniture tests, to measure the heat of a burning sofa by the oxygen missing from its smoke, without knowing what the sofa was made of.

Fat gives two and a half times the heat of sugar per gram, and less per litre of oxygen 🖖

Press Glucose, in the body and then Fat, in the body. The water stays liquid, as it does in you. Per kilogram, tripalmitin gives 39.15 MJ and glucose 15.57: 2.51 times as much, which is why fat is how animals store energy they have to carry. Per litre of oxygen it goes the other way: glucose gives 20.86 kJ and fat 19.45, about 6.8% less. The working in the litre row shows why: a mole of O₂ releases 467.50 kJ burning glucose and 435.94 burning fat. A metabolic cart in a hospital measures the carbon dioxide breathed out as well as the oxygen taken in for this reason: the ratio of the two says which fuel is burning, and the oxygen alone would be up to 7% out.

Acetylene breaks Thornton's rule because it arrives already holding 227.4 kJ/mol 🖖

Press Acetylene: 15.70 MJ per kilogram of oxygen, 19.88% above 13.1 and a quarter more than methane. Acetylene's formation enthalpy is +227.4 kJ/mol, energy put in when the molecule was made and handed back when it burns, on top of what the oxygen supplies. Take it away and acetylene's figure falls to 12.86, inside the band. Ethylene carries +52.4 and sits just outside, at 5.22% above. Hydrogen and carbon monoxide are further out still, 15.38% and 35.02% above, and neither is an organic compound, the class Thornton drew his rule from. Ammonia is not organic either and happens to land inside, 0.77% above. Graphite misses the other way, 6.12% under.

Problem solved in full

How much heat a resting body makes from its oxygen 4 steps
A resting adult takes up 0.250 litres of oxygen a minute, measured at 0 °C and 1 atm. What is their heat output in watts if the fuel is all glucose? If it is all fat? And how much is that in a day?

Open this problem in the tool
1. In the body the water stays liquid. Glucose then gives 20.86 kJ per litre of oxygen, and 0.250 litres a minute is 5.214 kJ a minute. Divided by 60 seconds, that is 86.9 W.
  
  $0.250 L/min \times 20.86 kJ/L = 5.214 kJ/min = \frac{5214 J}{60 s} = 86.9 W$
2. Fat, as tripalmitin, gives 19.45 kJ per litre: 4.862 kJ a minute, or 81.0 W.
  
  $0.250 L/min \times 19.45 kJ/L = 4.862 kJ/min = 81.0 W$
3. The two differ by 6.8%. Every real mixture of sugar and fat lies between them, so the oxygen alone pins the heat to within that range.
  
  $1 - \frac{81 . 0}{86 . 9} = 6 . 8%$
4. A day is 86,400 seconds. On glucose, 86.9 W is 7.51 MJ, or 1,795 kilocalories.
  
  $86.9 W \times 86, 400 s = 7.51 MJ = \frac{7 . 51 \times 1 0 ^{6}}{4184} = 1, 795 kcal$
Answer

86.9 W on glucose, 81.0 W on fat, 6.8% apart; about 7.5 MJ, or 1,795 kcal, a day. That is the order of a resting person's energy need, which is the point: a body at rest is a small heater, and its oxygen meter is its fuel gauge. Press Glucose, in the body and the per-litre row reads 20.86 kJ/L. What the page does not print is the carbon dioxide, and a real metabolic measurement needs it to know where between 81.0 and 86.9 the answer lies.

$81.0 W \leq P \leq 86.9 W \approx 7.5 MJ/day$

References (3)

Every heat of combustion and formation enthalpy on the page, fuel by fuel, each with the measurement it comes from: P. J. Linstrom and W. G. Mallard (eds.), NIST Chemistry WebBook, NIST Standard Reference Database Number 69. National Institute of Standards and Technology, Gaithersburg MD.
The 13.1 MJ per kilogram of oxygen, ±5%, that the page sets every fuel against: C. Huggett, "Estimation of rate of heat release by means of oxygen consumption measurements." Fire and Materials 4(2), 1980, pp. 61-65. DOI 10.1002/fam.810040202
How a fire laboratory turns the oxygen missing from its exhaust into a heat release rate, and the history back to Thornton's 1917 observation: J. C. Yang, "Detailed Derivations of Formulas for Heat Release Rate Calculations Revisited: A Pedagogical and Systematic Approach." Journal of Research of the National Institute of Standards and Technology 124, 124016, 2019. DOI 10.6028/jres.124.016