Heat capacity: definition, theoretical foundations, and thermal energy storage

Heat Capacity is defined by Robinson and Haas (1983) as the quantity of heat that is required to raise the temperature of a unit quantity of a given substance by one degree Kelvin at a constant pressure.

A brief history of the concept

Prior to the development of the modern theories of thermodynamics, it was widely thought that heat was some form of a fluid called calorific (Cengel, 2007).Different bodies were capable of effectively holding a certain quantity of this fluid and their ability to hold such a fluid was referred to as heat capacity as was initially investigated by one Joseph Black in 1750s (Laider,1993).In this age and time, we discuss the concept of the internal energy system. This comprises of microscopic kinetic as well as potential energy. Heat too is never considered as a fluid but is regarded as a transfer of energy which is disordered at a microscopic level.

Storage of thermal energy

Thermal energy is usually stored as kinetic energy in the rather random mode of translation in the monatomic substances as well as translations coupled with rotations of polyatomic molecules in the gaseous state.

Thermal energy may also be stored in the form of potential energy. This energy is closely associated with the higher modes of atomic vibrations in cases where they occur in a substance's interactomic bonds. A degree of freedom is however presented by the rotation, translation as well as any other combination of the various types of energy in vibration (potential and kinetic). There represent a degree of freedom of motion that is known to classically make part of the hat capacity of any given thermodynamic system.

On a microscopic scale, each and every particle in a given system effectively absorbs certain quantity of heat energy within the degree of freedom that it has. This form of absorption is noted to contribute in part to the specific heat capacity which in the classical sense of things approaches a mixum quantity per mole of particles as denoted by the Dulong-Pett law. This limit is usually 25 joules per Kelvin for every mole of atoms in a given crystalline structure.

Heat capacity, C of any given system is also noted to be the ratio of the heat that can either be added or effectively withdrawn from the given system in order to give rise to the resultant temperature.

C = ?Q/?T = dQ/dT [J/deg]

This type of definition is however noted to be valid in the absence of any form of phase transitions.

Heat Capacity is noted as the measure of a material's ability to absorb a given amount of thermal energy.

Thermal energy = the kinetic energy of the atomic motions +The potential energy of distortion of the interatomic bonds.

The higher the value of T, the larger the mean atomic velocity and corresponding the amplitude of the atomic vibrations. The outcome is the general rise in the level of thermal energy.

The temperature dependence of the concept of heat capacity

Heat capacity is noted to have a very weak temperature dependence at very high temperatures. This is noted to be true at temperatures that lie above the Debye temperature ?D.It however decreases towards zero as the value of T. approaches zero Kelvin.

The constant value of this quantity ( heat capacity) of several solids is referred to as the Dulong-Petit law. Sometimes in 1819, an experiment performed by Dulong and petite found that for several solids at room temperature, cv ? 25 JK-1mol-1.

This is noted to be consistent with the outcome or theoretical standings of the equipartition theorem of the classical mechanics theories which states that the energy which is added to solids are presented in the form of atomic vibrations with the potential and kinetic energy being associated with each atom's three degrees of freedom.

How the phase of a substance (ie solid, liquid, or gas) changes its heat capacity

Whenever a given material undergoes a change in phase such as from solid to liquid to gas, the heat capacity of such a material is never well defined and the material's heat capacity is technically indicated to be indefinite due to the fact that the heat goes into the given material but the material's temperature remains constant. Due to this fact, the meaning of heat capacity is often restricted to a single phase.

The explanation is that as a solid approaches liquid phase, it begins to soften while the frequency of the modes experience a drop. The heat capacity is therefore noted to increase.The hat capacity of a liquid is however noted to be a bit complex. This is due to the fact that there exists several local clusters of low energy vibration modes which can be excited thermally. The conversion of the substance's frequency modes to the rotational and translational modes is never straightforward.

How temperature is a measure of the kinetic energy of the molecules in a substance

Temperature is noted as a measure of the average kinetic energy of the atoms or molecules of a given substance expressed in terms of degrees that are designated on a standard scale (Mifflin,2000).