Specific heat capacity in the context of "Grey iron"

Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat that must be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). It quantifies the ability of a material or system to store thermal energy.

Heat capacity is an extensive property. The corresponding intensive property is the specific heat capacity, found by dividing the heat capacity of an object by its mass. Dividing the heat capacity by the amount of substance in moles yields its molar heat capacity. The volumetric heat capacity measures the heat capacity per volume. In architecture and civil engineering, the heat capacity of a building is often referred to as its thermal mass.

The lambda point is the temperature at which normal fluid helium (helium I) makes the transition to superfluid state (helium II). At pressure of 1 atmosphere, the transition occurs at approximately 2.17 K. The lowest pressure at which He-I and He-II can coexist is the vapor−He-I−He-II triple point at 2.1768 K (−270.9732 °C) and 5.0418 kPa (0.049759 atm), which is the "saturated vapor pressure" at that temperature (pure helium gas in thermal equilibrium over the liquid surface, in a hermetic container). The highest pressure at which He-I and He-II can coexist is the bcc−He-I−He-II triple point with a helium solid at 1.762 K (−271.388 °C), 29.725 atm (3,011.9 kPa).

The point's name derives from the graph (pictured) that results from plotting the specific heat capacity as a function of temperature (for a given pressure in the above range, in the example shown, at 1 atmosphere), which resembles the Greek letter lambda ${\displaystyle \lambda }$. The specific heat capacity has a sharp peak as the temperature approaches the lambda point. The tip of the peak is so sharp that a critical exponent characterizing the divergence of the heat capacity can be measured precisely only in zero gravity, to provide a uniform density over a substantial volume of fluid. Hence, the heat capacity was measured within 2 nK below the transition in an experiment included in a Space Shuttle payload in 1992.

A calorimeter is a device used for calorimetry, or the process of measuring the heat of chemical reactions or physical changes as well as heat capacity. Differential scanning calorimeters, isothermal micro calorimeters, titration calorimeters and accelerated rate calorimeters are among the most common types. A simple calorimeter just consists of a thermometer attached to a metal container full of water suspended above a combustion chamber. It is one of the measurement devices used in the study of thermodynamics, chemistry, and biochemistry.

To find the enthalpy change per mole of a substance A in a reaction between two substances A and B, the substances are separately added to a calorimeter and the initial and final temperatures (before the reaction has started and after it has finished) are noted. Multiplying the temperature change by the mass and specific heat capacities of the substances gives a value for the energy given off or absorbed during the reaction. Dividing the energy change by how many moles of A were present gives its enthalpy change of reaction.$${\displaystyle q=C_{\text{v}}(T_{f}-T_{i}),}$$ where q is the amount of heat according to the change in temperature measured in joules and C_v is the heat capacity of the calorimeter which is a value associated with each individual apparatus in units of energy per temperature (joules/kelvin).

The molar heat capacity of a chemical substance is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature. Alternatively, it is the heat capacity of a sample of the substance divided by the amount of substance of the sample; or also the specific heat capacity of the substance times its molar mass. The SI unit of molar heat capacity is joule per kelvin per mole, J⋅K⋅mol.

Like the specific heat, the measured molar heat capacity of a substance, especially a gas, may be significantly higher when the sample is allowed to expand as it is heated (at constant pressure, or isobaric) than when it is heated in a closed vessel that prevents expansion (at constant volume, or isochoric). The ratio between the two, however, is the same heat capacity ratio obtained from the corresponding specific heat capacities.

The volumetric heat capacity of a material is the heat capacity of a sample of the substance divided by the volume of the sample. It is the amount of energy that must be added, in the form of heat, to one unit of volume of the material in order to cause an increase of one unit in its temperature. The SI unit of volumetric heat capacity is joule per kelvin per cubic meter, J⋅K⋅m.

The volumetric heat capacity can also be expressed as the specific heat capacity (heat capacity per unit of mass, in J⋅K⋅kg) times the density of the substance (in kg/L, or g/mL). It is defined to serve as an intensive property.

Adair Crawford FRS FRSE (1748 – 29 July 1795), a chemist and physician, was a pioneer in the development of calorimetric methods for measuring the specific heat capacity of substances and the heat of chemical reactions. In his influential 1779 book "Experiments and Observations on Animal Heat", Crawford presented new experiments proving that respiratory gas exchange in animals is a combustion (two years after Antoine Lavoisier's influential "On combustion in general"). Crawford also was involved in the discovery of the element strontium.

In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in thermal equilibrium, energy is shared equally among all of its various forms; for example, the average kinetic energy per degree of freedom in translational motion of a molecule should equal that in rotational motion.

The equipartition theorem makes quantitative predictions. Like the virial theorem, it gives the total average kinetic and potential energies for a system at a given temperature, from which the system's heat capacity can be computed. However, equipartition also gives the average values of individual components of the energy, such as the kinetic energy of a particular particle or the potential energy of a single spring. For example, it predicts that every atom in a monatomic ideal gas has an average kinetic energy of ⁠3/2⁠k_BT in thermal equilibrium, where k_B is the Boltzmann constant and T is the (thermodynamic) temperature. More generally, equipartition can be applied to any classical system in thermal equilibrium, no matter how complicated. It can be used to derive the ideal gas law, and the Dulong–Petit law for the specific heat capacities of solids. The equipartition theorem can also be used to predict the properties of stars, even white dwarfs and neutron stars, since it holds even when relativistic effects are considered.