Unizor - Physics4Teens - Energy - Heat - Measuring
Channel: Zor Shekhtman on UNIZOR Education
Date: 2019-06-10

Unizor - Physics through a Looking Glass of Mathematician

Measuring Heat - Calorie

Heat and temperature were known and researched by scientists long before the molecular movement was determined as their essence. As a result, attempts of measuring the amount of heat were unrelated to kinetic energy of the molecules.

The unit of amount of heat was defined as amount of heat needed to increase the temperature of one gram of water by one degree Celsius (or Kelvin), and this unit of amount of heat was called a calorie (cal).

Obviously, this definition has its flaws. For example, the amount of heat needed to heat the same amount of water by the same temperature depends where exactly on Earth we are. The higher we are above the sea level - the less heat is needed. It also depends on the chemical purity of water. Also it's not obvious that the amount of heat needed to heat the water from 1°C to 2°C is the same as amount of heat needed to heat it from 88°C to 89°C, though within reasonable level of precision we do assume that this is true.

With the development of molecular theory of heat and establishing relationship between heat and kinetic energy of molecules there was a need to put into correspondence existing units of heat (calories) and units of mechanical energy (joules). A simple experiment allowed to do just that.

Imagine a standing on the ground large reservoir with known amount of water M of depth H from the surface to the bottom, kept at certain known temperature T°, and a relatively small stone of known mass m, having the same temperature T°, kept on the level of the surface of the water in a reservoir. This stone has certain known amount of potential energy E=m·g·H relatively to the bottom level of a reservoir.
Now we let the stone go down the reservoir to its bottom. Its potential energy relatively to the bottom of a reservoir decreases to zero. Where did the potential energy go? It's used to stir the water, thereby increasing the kinetic energy of its molecules.

Because of this more intense movement of molecules, the water will increase its temperature. Potential energy of a stone will turn into kinetic energy of the molecular movement of water. If the temperature of the water has risen by ΔT°, potential energy of a stone m·g·H (in joules) equals to M·ΔT (in calories).

Precise experiments like the above allowed to determine the correspondence between historical measure of the amount of heat in calories under different conditions and contemporary one in units of energy in SI - joules. This correspondence had been established approximately as
1 calorie = 4.184 joules
but under different conditions (initial temperature, air pressure etc.) it might be equal to a slightly different value.

Besides calorie, which is a relatively small amount of heat, the unit kilocalorie (kcal) had been introduced.
As is obvious from its name, 1 kilocalorie = 1000 calories.

The amount of energy contained in food and in some other practical cases very often is measured in kilocalories, which sometimes are called large calories, while a calorie is sometimes called small calorie. Unfortunately, the word "large" in many cases is omitted, which might cause misunderstanding.
From the experimental viewpoint, 1 kcal is amount of heat needed to heat 1 kg of water by one degree Celsius (or Kelvin).

To avoid problems with the definition of calorie as amount of heat needed to warm up one gram of water by one degree Celsius, the contemporary scientific definition of thermocalorie is
1 thermocalorie = 4.1833 joules