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In chemistry, heat amounts were often measured in calories. Confusingly, there are two common units with that name, respectively denoted cal and Cal: the small calorie (gram-calorie, cal) is 4.184 J exactly. It was originally defined so that the specific heat capacity of liquid water would be 1 cal/(°C⋅g).
A closely related property of a substance is the heat capacity per mole of atoms, or atom-molar heat capacity, in which the heat capacity of the sample is divided by the number of moles of atoms instead of moles of molecules. So, for example, the atom-molar heat capacity of water is 1/3 of its molar heat capacity, namely 25.3 J⋅K −1 ⋅mol ...
Note that the especially high molar values, as for paraffin, gasoline, water and ammonia, result from calculating specific heats in terms of moles of molecules. If specific heat is expressed per mole of atoms for these substances, none of the constant-volume values exceed, to any large extent, the theoretical Dulong–Petit limit of 25 J⋅mol ...
The molar heat capacity is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the specific heat capacity, often called simply specific heat, is the heat capacity per unit mass of a material. Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under ...
Molar heat capacity of most elements at 25 °C is in the range between 2.8 R and 3.4 R: Plot as a function of atomic number with a y range from 22.5 to 30 J/mol K.. The Dulong–Petit law, a thermodynamic law proposed by French physicists Pierre Louis Dulong and Alexis Thérèse Petit, states that the classical expression for the molar specific heat capacity of certain chemical elements is ...
If heat capacity is measured for a well-defined amount of substance, the specific heat is the measure of the heat required to increase the temperature of such a unit quantity by one unit of temperature. For example, raising the temperature of water by one kelvin (equal to one degree Celsius) requires 4186 joules per kilogram (J/kg).
In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region. Since then, the ...
For an ideal gas, the molar heat capacity is at most a function of temperature, since the internal energy is solely a function of temperature for a closed system, i.e., = (,), where n is the amount of substance in moles.