The Physics
Opus in profectus

Sensible Heat

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Heat that results in a temperature change is said to be "sensible" (although this term is falling out of favor). This is because it can be "sensed" I assume.

1781 Wilcke comes up with the concept of specific heats.

1819 Objects have a heat capacity, while materials have a specific heat capacity (often just called specific heat) was first defined by Pierre-Louis Dulong and Alexis-Thérèse Petit, France, 1819.

The specific heat capacity (which is often shortened to specific heat) of a material is the amount of heat required to change a unit mass of a substance by one unit of temperature.

Q = mcT


Q =  heat evolved (+ heat absorbed, − heat released) [J]
m =  mass [kg]
c =  specific heat capacity [J/kg°C or J/kgK]
T =  temperature change [°C or K]
Specific heat capacity at constant pressure for selected materials
(~300 K and ~100 kPa except where otherwise indicated).
material cp (J/kg K) material cp (J/kg K)
air, 200 K 1650   mica 880
air, 300 K 1158   milk, cow, whole 3850
air, 500 K 1073   neon 1030
air, 1,000 K 1151   nickel 444
alcohol, methyl (wood) 2530   nitrogen (N2) 1040
alcohol, ethyl (grain) 2440   oil, olive 1790
aluminum 897   oxygen (O2) 918
ammonia, liquid 4700   perlite 387
ammonia, gas 2060   platinum 133
argon 520   plutonium 140
asphalt 920   porcelain 1085
bone 440   salt 880
brass 375   sand 835
brick 840   scandium 568
concrete 880   silicon 705
carbon, diamond 516   silver 235
carbon, graphite 717   soil, dry 800
copper 385   soil, wet 1480
eggs, chicken 3180   snow 2090
freon 12, liquid 871   teflon 1172
freon 12, vapor 595   tin 228
glass, crown 670   titanium 523
glass, flint 503   tungsten 132
glass, pyrex 753   uranium 116
gold 129   water, ice, −5 °C 2090
granite 790   water, liquid, 0 °C 4217.6
gypsum 1090   water, liquid, 20 °C 4181.8
hydrogen (H2) 14,304   water, liquid, 40 °C 4178.5
helium 5193   water, liquid, 60 °C 4184.3
iron 449   water, liquid, 80 °C 4196.3
lead 129   water, liquid, 100 °C 4215.9
lithium 3582   water, vapor, 0 °C 3909.2
lucite 1460   water, vapor, 27°C 3984.6
marble 880   water, vapor, 100 °C 4039.2
mercury 140   wood 1700
      zinc 388

water has an unusually high specific heat, the only natural substance with a higher specific heat is liquid ammonia


A calorie is the energy needed to raise the temperature of one gram of water by one celsius degree. This turns out to be a terrible definition as the heat required to raise the temperature of any substance varies with temperature itself.

Scatterplot with curve fit

The specific heat of liquid water varies with temperature.

Thus, there are at least five different units that are called calories. Three of them are now defined in terms of the SI unit of energy, the joule.

Many people, especially residents of the United States, associate the word "calories" with a number describing some dietary characteristic of the foods they eat. These calories are not the same as the unit I just described. A "dietetic calorie" or "food calorie" is equal to one thousand of these "regular calories". The quantity found on product labels is actually a kilocalorie or a kilogram calorie (since 1000 calories is enough energy to raise the temperature of one kilogram of water by one celsius degree). To distinguish these two units in print, it is often recommended that "regular calories" begin with a lowercase "c" and "food calories" an uppercase "C"; that is, "calories" for the classroom and "Calories" for the lunchroom, but hardly anyone obeys this rule.

I recommend that the whole notion of calories be discarded altogether.

  1. The scientific definition is so poorly standardized that no one knows what you mean when you say "calorie" without specifying. A calorie measured a what temperature? 15 °C? 20 °C? Should we average the results for every temperature at which water is a liquid? Everyone of these has been used at one time.
  2. There are two hugely different units with exactly the same name. A "food calorie" is a thousand times larger than a "regular calorie". To me this is as bad as using the word "inflammable" (which should mean something that can't catch fire) to mean "flammable" (which means something that can catch fire).

The calorie had its time. It should now die quietly.

There is more than one kind of calorie.
type of calorie joule equivalent SI status
thermochemical 4.184 defined
International Table 4.1868 defined
at 15 °C 4.1855 defined
at 20 °C 4.1818 approximate
mean 4.19092 approximate

british thermal units

From the "mechanical equivalent of heat" to the "specific heat capacity of water"

A British thermal unit (Btu or BTU and also known as a heat unit in the United States) is the energy needed to raise the temperature of one pound of water by one fahrenheit degree. Like the calorie, there are several different types of Btu, each based on a different initial temperature. The most common are the thermochemical Btu (approximately equal to 1054.350 J) and the International Table Btu (equal to 1055.05585262 J by definition), but there are a few more.

One hundred thousand (105) Btu are called a therm. Since there are several definitions of the Btu, there are several definitions of the therm. In the United States one therm equals 105.4804 MJ while in Europe it equals 105.5060 MJ. The therm is commonly used by natural gas utilities. Burning 2.75 cubic meters of natural gas releases about one therm of energy in the form of heat. This volume is only approximate, however. Natural gas is a natural substance, which means that it varies in composition. Different wells produce natural gas with different energy contents.

In the United States, 1015 is called a quadrillion and 1015 Btu is called a quad (short for a quadrillion Btu). Nationwide and worldwide energy statistics are often quoted in this unit. One quad is approximately 1.055 × 1018 J or about one exajoule.


Mass specific heats vary significantly with material, but molar specific heats are rather similar. This empirical relationship is known as the Law of Dulong and Petit (1819) after its co discoverers Pierre Louis Dulong (1785–1838) and Aléxis Thérèse Petit (1791–1820) of France. (An interesting aside: Dulong accidentally lost an eye when he discovered nitrogen trichloride.)

Specific heat and atomic mass are almost inversely proportional and vary significantly with material. Hydrogen, helium, and lithium; which have the smallest masses; have such large specific heat capacities that they do not fit on this graph. Molar specific heats, on the other hand, are relatively constant.

Side by side scatterplots with curve fits

There are LAWS (like Newton's laws of motion or the conservation of energy) and there are "laws" (like Hooke's law and the law of Dulong and Petit).