# Food energy **Food energy** is the [[Chemical_energy|chemical energy]] that animals extract from food by [[Cellular_respiration|respiration]] — formally, the [[Gibbs_free_energy|Gibbs free energy]] released when the food's carbon and hydrogen are oxidised to carbon dioxide and water, which is the `H - T S` row in the standard table of energy forms.[^murphy-forms] It is quoted in kilocalories or kilojoules, and the conversion is exact by definition: 1 cal = 4.184 J, so 1 kcal = 4,184 J.[^murphy-cal] In the microsim below the reader loads a day's intake and then spends it on activities from the Portal Book's table, watching two readings at once — the [[Power_(physics)|power]] the body is drawing right now, and the running total of [[Energy|energy]] taken in against energy spent. The arithmetic that anchors the whole display is one line: a 2,000 kcal daily intake is 8.368 MJ over 86,400 seconds, which is 96.85 W — in the book's words, "very close to 100 W".[^murphy-97w] On the Energy flagship's spine this page is the main article for Part IV — Scientific use, section *Humans*, and its sim is the person preset of the [[Joule|joule]] odometer: power is the speedometer, energy the odometer, and a human being is a 100 W appliance that has to be refuelled three times a day. It hands on to [[Basal_metabolic_rate|basal metabolic rate]] for the resting floor and to [[Calorie|the calorie]] for the unit's own tangled history. Two warnings belong in the lead because they govern everything below. The first is that food energy and the heating of water share their units but not their physics: you cannot eat a joule of hot water, and the fact that a day's food would raise a bathtub's temperature is a unit conversion, not a metabolic statement.[^murphy-falseprec] The second is precision. The 96.85 W above is arithmetic done on a round number; the book explicitly calls displaying it to four figures false precision, and the sim rounds it to 97 W or simply says "about 100 W".[^murphy-falseprec] ## History and methods of measurement The measurement problem has always been the same: how much energy is in this food, and how much of it does the eater actually get? The two questions have different answers, and the history of the subject is the history of learning that they differ. The unit came first, and it came from water. A calorie was defined as the heat needed to raise the temperature of one gram of water by one degree Celsius, which fixes its relation to the mechanical unit at 1 cal = 4.184 J and 1 kcal = 4,184 J exactly.[^murphy-cal] Because the definition is a [[Heat_capacity|heat-capacity]] statement, everything about food measurement inherited the vocabulary of [[Calorimetry|calorimetry]] — and inherited, with it, the standing confusion between the small calorie and the "Calorie" of the dinner table, which is a kilocalorie. The first quantitative answers came from burning food and measuring the heat, and the correction to those answers came from measuring what left the body unburned. The second approach — total combustion heat minus what is not absorbed and not metabolised — is the one still used to compute the numbers printed on packaging. ### Direct calorimetry of combustion The direct method is to burn a dried sample completely in oxygen inside a sealed vessel immersed in a known mass of water, and to infer the [[Heat_of_combustion|heat of combustion]] from the water's temperature rise. The instrument is a [[Calorimeter|bomb calorimeter]], and the calculation is the calorie's own definition run backwards: mass times [[Specific_heat_capacity|specific heat capacity]] times temperature change. The Portal Book's worked examples are exactly this arithmetic at kitchen scale. Warming 30 g of water by 5 °C takes 150 cal, about 628 J. Warming 2 kg by 20 °C takes 40 kcal. Warming a 250 g cup by 35 °C takes 8.75 kcal, about 36 kJ — and that last one is a useful calibration for anyone reading a nutrition label, because a cup of tea warmed from tap temperature costs roughly as much energy as a bite of biscuit.[^murphy-cal] Raising half a kilogram of water from 20 °C to 100 °C takes 40 kcal, or 167 kJ, which a 1,000 W kettle supplies in 167 seconds.[^murphy-cal] What the bomb measures is the full [[Enthalpy|enthalpy]] of [[Combustion|combustion]], the same quantity that would be released by burning the food in a fire. At the molecular level this is bond chemistry with a characteristic scale: burning 12 g of carbon releases 394 kJ, which over Avogadro's number of atoms is 6.5 × 10⁻¹⁹ J per atom — about 4 eV, or roughly 1 eV per carbon–oxygen bond formed.[^murphy-bond] Chemical energy storage of every kind, food included, lives near 10 kcal per gram at its densest, which is the ceiling that separates chemical fuels from nuclear ones by a factor near a million.[^murphy-chemdens] ### The Atwater system The bomb overstates what an eater receives, for three reasons that are all losses rather than errors. Some of the food is not digested and leaves unchanged. Some of what is absorbed is not fully oxidised — nitrogen-bearing compounds in particular leave the body as urea rather than as nitrogen oxides, taking unreleased energy with them. And some energy is spent on the digestion itself. The system in use replaces per-food measurement with per-macronutrient factors: the mass of carbohydrate, fat and protein in a food is multiplied by a fixed energy value for each, and the products are summed. The conventional rounded factors are about 4, 9 and 4 kcal per gram for carbohydrate, fat and protein respectively, with about 7 kcal per gram for ethanol.[citation needed] The factors are averages over classes of compounds, not properties of any single molecule, which is why two foods with identical printed energy can differ in what they actually deliver. The system's virtue is that it is additive and cheap: a laboratory measures composition, not combustion, and the energy follows by arithmetic. Its limitation is that it assumes a standard digestive efficiency for each class, which is a population average. For the purposes of this article's microsim the consequence is simple — the intake side of the odometer is always a convention, while the expenditure side is a measurement, and the two are not equally certain. ## Dietary sources of energy Three classes of compound supply essentially all of it. Fat is the densest, at roughly twice the energy per gram of the other two, because its carbon is the most reduced — there is more hydrogen to oxidise and less oxygen already attached. Carbohydrate is partly oxidised already, which is why it yields less per gram, and protein yields about the same as carbohydrate while also serving as structural material, so using it as fuel is a second-best use of an expensive input. Ethanol sits between fat and carbohydrate and supplies energy with no other nutritional role. The pattern is not biological but chemical, and the same rule orders every fuel: the energy released on combustion rises with the hydrogen-to-oxygen ratio of the starting material. It is the reason methane beats coal per kilogram, the reason fat beats sugar, and the reason a [[Biomass|biomass]] feedstock must be chemically upgraded before it becomes a competitive [[Biofuel|biofuel]]. All of these fuels, food included, are the stored output of [[Photosynthesis|photosynthesis]]; food energy is solar energy that has been through one or more biological transfers, and each transfer costs. Within the body the [[Redox|redox]] chemistry is run in small steps rather than in a flame, with the free energy captured in [[Adenosine_triphosphate|ATP]] rather than released as heat, which is what makes an organism a [[Energy_conversion_efficiency|converter]] rather than a stove. The total is the same either way — that is [[Conservation_of_energy|conservation of energy]] — but the fraction available as work rather than heat is not. ## Energy usage in the human body This is the section the article's microsim belongs to. Its central number is the one in the lead: 2,000 kcal per day is 8.368 MJ, and dividing by the 86,400 seconds in a day gives 96.85 W — a figure the book immediately rounds, calling four significant figures false precision.[^murphy-97w][^murphy-falseprec] A person is a 100 W appliance. That single comparison does more work than any other in energy literacy, because it makes a human body commensurable with everything else on the power ladder. A 100 W continuous draw is 2.4 kWh a day, which is 8.6 MJ, which is the food. Against it, the average resident of the United States commands about 10,000 W once industry, transport and buildings are counted in — roughly a hundred times the metabolic rate, which is the same as saying that each person is served by about a hundred invisible people's worth of energy.[^murphy-scale] The body is about one per cent of a modern person's energy footprint. The reader's control in the sim is the Portal Book's activity table, which gives energy costs for a set of everyday actions in joules.[^murphy-table51] Selecting activities fills the day, and the two readouts move together: instantaneous power on the speedometer, cumulative energy on the odometer, with intake drawn as a second line so that the gap between the two is visible at every moment. The table's own caveat is displayed with it — its values are illustrative, "not definitive or exact", and the sim shows them as round numbers or ranges rather than as precise quantities.[^murphy-table51] A second readout puts the day's food into thermal units, which is where the lead's warning earns its place. The energy in about 2,000 kcal is 8.37 MJ, and the book's own bathtub example makes the same quantity concrete: heating 57 kg of water through 35 °C takes 1,995 kcal, about 8.35 MJ — essentially one day's food — and a 30,000 Btu/hr heater, which is 8,800 W, takes about 950 seconds to do it.[^murphy-bath] The numbers match because the units match. The physics does not: a body cannot use food as a heater's fuel, and a heater cannot run on food.[^murphy-falseprec] ## Recommended daily intake The 2,000 kcal figure that anchors the sim is a labelling convention rather than a prescription. It exists so that the percentages on a package have a fixed denominator, and the whole point of a fixed denominator is that it is the same for everyone reading the label — which means it is right for almost no one. The actual requirement is the sum of a resting floor and an activity term. The floor is the [[Basal_metabolic_rate|basal metabolic rate]], the power needed to run the body at rest, and it scales with body mass more slowly than proportionally, so a heavier person needs more total energy but less per kilogram. The activity term is what the microsim's table adds, and it is the part a person can change: the same body at the same mass can span a wide range of daily totals depending on what it spends its hours doing. Three practical consequences follow from treating intake as a power rather than a quantity. A steady surplus of even a few watts accumulates: 100 kcal a day is 418 kJ, which is under 5 W, and yet it is about 150,000 kJ a year. Short-term intake is irrelevant to that arithmetic, since the body buffers over days. And because both sides of the balance are uncertain — the intake side by the Atwater convention, the expenditure side by individual variation — the honest use of these numbers is to compare a person against themselves over time, not against a table. ## Nutrition labels Labels report food energy in kilocalories, in kilojoules, or in both, and the conversion between them is the exact one given above: 1 kcal = 4,184 J, so 2,000 kcal = 8.368 MJ.[^murphy-cal] The unit ladder that connects those to the rest of the energy system is worth having to hand, because most arguments about food energy are lost in units rather than in physiology: 1 kWh = 3.6 MJ, 1 [[British_thermal_unit|Btu]] ≈ 1,055 J, and 10,000 kcal = 41.84 MJ ≈ 40,000 Btu = 0.4 therm, which is about 40 cubic feet of natural gas.[^murphy-power][^murphy-scale][^murphy-therm] The capitalisation trap is worth stating plainly. A dietary "Calorie", with a capital C, is a kilocalorie — one thousand of the physicists' calories. Labels in most jurisdictions print the kilocalorie value and label it "kcal" or "Calories", so the figure is the same; the ambiguity only bites when a reader carries a label number into a physics calculation without converting. Two further label conventions matter for anyone using printed values as data. Figures are rounded, often to the nearest 10 kcal, so a small item's stated energy can be a substantial fraction wrong in either direction. And the value is computed from measured composition through fixed factors, not measured on that batch, so its uncertainty is structural rather than statistical. In [[Thermodynamics|thermodynamic]] terms a label reports an enthalpy change estimated for a standard digester; in [[First_law_of_thermodynamics|first-law]] terms it is one side of an energy balance whose other side — the work done, the heat lost, the change in [[Internal_energy|internal energy]] stored — is never printed anywhere.[^yan-first] ## See also - [[Basal_metabolic_rate]] - [[Calorie]] - [[Calorimetry]] - [[Heat_of_combustion]] - [[Cellular_respiration]] - [[Photosynthesis]] - [[Joule]] - [[Chemical_energy]] ## References [^murphy-forms]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097, Chapter 5 Energy and Fossil Fuels, p. 90, Table 5.2 (the energy forms and where each reappears: `H − TS` for chemical, `hν` for solar, `m g h` for hydro and tidal, `½mv²` for wind, `c_p m ΔT` for thermal, `qV` for electric, `mc²` for nuclear). https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet [^murphy-cal]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097, Chapter 5 Energy and Fossil Fuels, pp. 93–94 (1 cal = 4.184 J and 1 kcal = 4,184 J; 30 g of water through 5 °C = 150 cal ≈ 628 J; 40 kcal heats 2 kg by 20 °C; 250 g through 35 °C = 8.75 kcal ≈ 36 kJ; 0.5 kg from 20 °C to 100 °C = 40 kcal = 167 kJ, or 167 s at 1,000 W). [^murphy-97w]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097, Chapter 5 Energy and Fossil Fuels, pp. 94–95 (2,000 kcal/day = 8.368 MJ ÷ 86,400 s = 96.85 W, "very close to 100 W"). [^murphy-falseprec]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097, Chapter 5 Energy and Fossil Fuels, p. 95 (the book's own caution against displaying 96.85 W to four significant figures as false precision; and that food energy and water heating share units but not physics). [^murphy-table51]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097, Chapter 5 Energy and Fossil Fuels, p. 89, Table 5.1 (energy costs of everyday activities in joules; the book states that Table 5.1 and Fig. 5.2 values are illustrative, "not definitive or exact", pp. 89, 92). [^murphy-bath]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097, Chapter 5 Energy and Fossil Fuels, pp. 95–96 (heating 125 lb of water through 63 °F takes 7,900 Btu, "just over 15 minutes" at 30,000 Btu/hr = 8,800 W; the metric check 57 kg through 35 °C = 1,995 kcal ≈ 8.35 MJ, ≈950 s. The tightened values 15.75 min and 948.5 s are computed in the Wikitube extract from the book's own inputs). [^murphy-scale]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097, Chapter 5 Energy and Fossil Fuels, p. 95 (1 Btu ≈ 1,055 J; 1 quad ≈ 1.055 × 10¹⁸ J; 1 yr ≈ 3.16 × 10⁷ s; the United States uses ≈100 quads/yr ≈ 3 TW ≈ 10,000 W per person). [^murphy-power]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097, Chapter 5 Energy and Fossil Fuels, pp. 91–93 (1 W = 1 J/s; 1 kWh = 1,000 J/s × 3,600 s = 3.6 MJ; power is the speedometer and energy the odometer; "never label anything kW per hour"). [^murphy-therm]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097, Chapter 5 Energy and Fossil Fuels, p. 96 (10,000 kcal = 41.84 MJ ≈ 40,000 Btu = 0.4 therm ≈ 40 ft³ of natural gas, or a little under half a gallon of propane; 1 therm = 10⁵ Btu = 1.055 × 10⁸ J = 29.3 kWh). [^murphy-bond]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097, Chapter 5 Energy and Fossil Fuels, p. 98 (combustion releases 394 kJ per 12 g of carbon; divided by 6 × 10²³ that is 6.5 × 10⁻¹⁹ J ≈ 4 eV per atom, about 1 eV per carbon–oxygen bond; 1 eV = 1.6 × 10⁻¹⁹ J). [^murphy-chemdens]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097, Chapter 6 Alternative Energy, pp. 273–274 (chemical energy density is of order 10 kcal/g, against 16.8 × 10⁶ kcal/g for fission). [^yan-first]: Yan, Claire Yu (2022). *Introduction to Engineering Thermodynamics*. Portal Book 115, Chapter 4 The First Law of Thermodynamics for Closed Systems, pp. 127–186 (page to pin) (the closed-system energy balance in which stored internal energy, work done and heat exchanged must sum). https://open.umn.edu/opentextbooks/textbooks/introduction-to-engineering-thermodynamics ## External links - *Energy and Human Ambitions on a Finite Planet* (2021), Portal Book 097 — Open Textbook Library record: https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet - *Introduction to Engineering Thermodynamics* (2022), Portal Book 115 — Open Textbook Library record: https://open.umn.edu/opentextbooks/textbooks/introduction-to-engineering-thermodynamics - The Wikipedia pair's External links section lists the pair's own links, including the national food-composition databases and labelling regulations behind the Atwater factors and the Nutrition labels section. <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Food_energy.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Food energy* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Food_energy.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Food_energy.html" data-title="Food energy"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Food_energy) : [Wikitube](https://en.wikitube.io/wiki/Food_energy) · pinned revision [1370336058](https://en.wikipedia.org/w/index.php?oldid=1370336058) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Energy]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Energy row E24 · sim pending (matter/Food_energy).*