Heat capacity

The heat capacity of the body indicates how much thermal energy it receives, based on the temperature change or write:

The heat capacity is an extensive quantity. The unit ( Joules per Kelvin).

The converted energy is generally dependent on the process control of the temperature change from. One therefore defines in particular the heat capacity at constant pressure and the heat capacity at constant volume. Except for gases but the difference is usually negligible.

The heat capacity of a body is determined with the aid of a calorimeter, for example, differential scanning calorimetry (DSC). If no measured values ​​are available in many materials, the heat capacity as the Benson method can be estimated using group contribution methods.

Calculation

For the average value of the heat capacity between the initial and final temperatures is true:

For accurate observation is the heat capacity defined because of the possible temperature dependence as:

Neither the chemical composition nor the amount of substance of the body may be changed thereby. Energy sales at constant temperature, such as phase transformation ( melting, evaporation ) or in a chemical reaction with heat of reaction, are excluded.

Types of heat capacity

If the substance of the body chemically and physically homogeneous, so it makes sense to convert the heat capacity in one of the following intensive variables:

• Specific heat capacity, related to the mass heat capacity. unit:
• Molar heat capacity (including heat capacity ), which related to the molar heat capacity. unit:
• Of heat storage, the volume-based heat capacity. unit:

The specific and molar heat capacity are available for a given material composition in a fixed ratio:

Wherein the molar mass (if the average molar mass ) of the substance in question. Therefore, it is sometimes addressed (eg physical textbooks ) and the molar heat capacity and specific heat capacity. For a more detailed physical examination of the concept, in particular on measured values ​​and physical model concepts, see specific heat capacity.

Related to thermodynamic state variables

Based on the state variables of volume, pressure and internal energy of the body and the first main theorem is the heat capacity at constant volume

At constant pressure, the volume may change with temperature, so that the energy content of the body is indicated by the enthalpy. For the heat capacity follows

Note that the exchanged heat is not a state variable, but after the 2nd law leads to a certain change in the state variable entropy in accordance with, provided that the heat exchange is reversible. because of

Also applies

It is with the internal energy and enthalpy with. Using the second law of thermodynamics can be derived more:

Here, the thermal expansion coefficient, the isothermal compressibility and isentropic adiabatic compressibility and the isentropic exponent is the absolute temperature therefore is always ( and, for example, for water in the range of density anomaly at temperatures 0-4 ° C, supra).

Heat capacity of an ideal gas at constant pressure and at constant volume

According to the thermodynamic definition of the ideal gas with the thermal state equation: ( the universal gas constant). Thus, and therefore

This difference is exactly explained by that in a ( infinitesimally small ) heating at constant pressure at first only the internal energy is increased by, and then increases the volume, which the displacement work requires. According to the caloric of the ideal gas equation of state at a constant temperature does not depend on the volume of the internal energy, so that the overall power conversion is given by. It follows from the above relation between the two specific heats. The independence of the internal energy of the volume followed in turn by the second law of thermodynamics from the thermal equation of state. It is experimentally demonstrated by the Überströmversuch of Gay -Lussac (1807 ).

Theoretical predictions for individually can not be derived from classical thermodynamics, but only from the statistical mechanics based on models for the construction of the substances made ​​of atoms and molecules. For monatomic ideal gas results in, for example, exactly. For details, refer under specific heat capacity.

Negative heat capacity

Only systems with a positive heat capacity are stable in the thermodynamic sense. However, there are unstable systems, which are hot as a result of energy delivery. This is for instance the interstellar gas clouds and some stars whose gravitational binding energy by the virial theorem twice as large as the total internal kinetic energy. An increase in the binding energy, such as radiation, therefore, shows only half as radiated energy and the other half as an increase of the kinetic energy of the particles. The contracting system is thus from energy and is still hot, what one is formally as a negative heat capacity. Even very small systems (English cluster ) from a few hundred atoms close to a phase transition show this behavior. For gravitating systems, the further contraction can be prevented if within new energy sources such as ignite nuclear fusion. To reach a steady state the same amount of energy must then be released in the interior as a result of the temperature and size of the surface is irradiated. For main sequence stars, this is the case, while the variable Mira stars oscillate between contraction and expansion.