Heat capacity: definition, measurement, and applications

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.

The theory of heat capacity

Heat capacity (C) a term which is otherwise referred to as thermal capacity is the physical quantity which is measurable and that characterizes the amount of heat that is required in order to change the temperature of a substance by a specific amount. In terms of the International Systems of Unites (SI), the concept of heat capacity is denoted in unites of joule(s) (J) per kelvin (K).

There are several derived quantities that are used in the specification of the concept of heat capacity as a physical quantity with intensive property. This is to say that the quantity is expressed as an independent one in regard to the sample size. These are known as molar heat capacity a concept which refers to the heat capacity per mole of a given pure substance, Specific heat capacity on the other hand refers to the heat capacity per nit mass of any given material.

In certain occasions within the engineering context, the concept of volumetric heat capacity is employed. Temperature on the other hand expresses the average kinetic energy of a given particulate matter. Heat is however the transfer of thermal energy and denotes a floe of this energy from a region of high temperature to a region of low temperature.

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