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## Elementary Thermodynamics - Heat

• calorie

• kilocalorie (or “dietary calorie”)

• British Thermal Unit (BTU)

A calorie or heat is defined as the amount of thermal energy transfer required to change the temperature of one gram of water by one degree Celsius (same temperature change as one Kelvin). One calorie is equivalent to 4.186 joules.

A British Thermal Unit, or BTU is defined as the amount of thermal energy transfer required to change the temperature of one pound of water by one degree Fahrenheit (same temperature change as one degree Rankine). One BTU is equivalent to 778.2 foot-pounds.

The unit of “dietary” calories is used to express the amount of thermal energy available in a sample of food by combustion_{1}. Since the official unit of the “calorie” is so small compared to the typical amounts of energy contained in a meal, nutritionists use the unit of the kilocalorie (1000 calories, or 4186 joules) and call it “Calorie” (with a capital letter “C”).

Just as “Calories” are used to rate the energy content of food, the heat units of “calories” and “BTU” are very useful in describing the potency of various industrial fuels. The following table shows the heat of combustion for a few common fuels, in units of kilocalories per gram and BTU per pound:

Fuel |
Combustion heat (kcal/g) |
Combustion heat (BTU/lb) |

Methane (CH4) |
13.3 |
23,940 |

Methanol (CH4O) |
5.43 |
9,767 |

Ethanol (C2H6O) |
7.10 |
12,783 |

Propane (C3H8) |
12.1 |
21,700 |

Carbon monoxide (CO) |
2.415 |
4,347 |

For example, if exactly one gram of methane gas were completely burnt, the resulting heat transfer to water would be sufficient to warm 13.3 kilograms of water from 20 degrees Celsius to 21 degrees Celsius (a temperature rise of one degree Celsius).

If a meal rated at 900 Calories (900 “dietary calories,” or 900 kilocalories) of energy is metabolized, the resulting heat would be sufficient to warm a pool of water 900 kilograms in mass (900 liters, or about 237 gallons) by one degree Celsius. This same amount of heat could raise half the amount of water twice the temperature rise: 450 liters of water warmed two degrees Celsius.

_{1}Animals process food by performing a very slow version of combustion, whereby the carbon and hydrogen atoms in the food join with oxygen atoms inhaled to produce water and carbon dioxide gas (plus energy). Although it may seem strange to rate the energy content of food by measuring how much heat it gives off when burnt, burning is just a faster method of energy extraction than the relatively slow processes of biological metabolism.

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