SPECIFIC HEAT

Internal energy is not measurable. For systems of single phase substances, specific heats provide a means of relating internal energy (non-measurable) changes to the changes of measurable properties of the substance; pressure, temperature and specific volume.

Basic Thermodynamics ~ J. Pohl © www.THERMOspokenhere.com

SPECIFIC HEAT

Internal energy is not measurable. For systems of single phase substances, specific heats provide a means of relating internal energy (non-measurable) changes to the changes of measurable properties of the substance; pressure, temperature and specific volume.

Internal energy is not measurable. For systems of single phase substances, specific heats provide a means of relating internal energy (non-measurable) changes to the changes of measurable properties of the substance; pressure, temperature and specific volume.

By way of background, the state of a gas, for example, can be represented as a three dimensional relationship or surface; F(p,v,T) = 0. Thus were one to select values, p*, and T*, then impose these conditions upon the substance, by its molecular structure, the substance would select its preferred, v*. Put in functional notation, v = v(p,T). Extension of such relationships requires calculus of two variables, some of which we use in explanation of how internal energy is made quantitative.

The traditional two measurable variables associated with internal energy are: temperature and specific volume, u = u( T, v ). The total differential of internal energy, du, is written:

The coefficient, (partial u / partial T)v represents the change of the internal energy with change of its temperature while specific volume is constant. This partial derivative is named the specific heat at constant volume and is written as cv (spoken as "c - sub - v"). We make the substitution into the above.

Immediately above, du is integrated (symbolically) to obtain a Δu. How to manipulate the second integrand so it can be integrated is an advanced topic. However, we notice that the integral will be zero for any substance event with constant specific volume. The is, if v = constant, then dv = 0. Solids and liquids are reasonably approximated as having constant density. Thus (with use of the mean value theorem) we have:

The specific heats of condensed phases (liquids and solids) vary with temperature. Careful, second-level analysis must account for this. However, in preliminary calculations, it is expedient to use the mean value theorem, and an approximated value for the specific heat. Values of specific heats are provided where needed.