THERMO Spoken Here! ~ J. Pohl © ( C4200~2/15)

3.10 Energy: SUBSTANCE

The general ideas of internal energy and compression of a substance arrive early in science education. Our goal is to give form to those ideas and a representation for them suitable for a thermodynamic energy equation. Our extrinsic equation addressed system displacement, kinetic and potential energies. Our immediate task is to identify and explain internal energy and compression work which are associated not with system displacement but with its deformation.

INTERNAL ENERGY: Suppose the collective energy of a fluid composed of a googol of small entities, that is molecules, with each of behaving as a BODY. Could the energy of that group be written as two pieces, one kinetic in nature, the other potential:

(1) 1

The kinetic energy portion of the gas energy would likely be the sum of kinetic energies of all of the particles. With their masses as m_i and their speeds as, v_i, this is written:

(2) 2

While none of the information required to effect the above calculation can be known, all is not lost. Some of the energy it represents can be made quantitative, made measurable "in the whole" by definition of the "center of mass." The position of the center of mass can often be measured and so also can its velocity. This means the bulk, or overall kinetic and potential energy of the particles can be quantified. This idea is introduced into the expression for sum of kinetic energies by use of the definition of particle position in relation to the position of the center of mass:

P_i(t) = P(t)_c.m.,gas + P_{i /c.m.}(t).

(3) 3

When particle velocity (the derivative of position) is substituted into the expression for kinetic energy. The sum of kinetic energies of all particles can be cast as being three components. Two of the components, linear kinetic energy and a rotational kinetic energy can be quantified in terms of the mass of the gas and the velocity of its center of mass. The third component, the sum of the particle kinetic energies relative to the center of mass, is not measurable. This term is designated as the kinetic component of internal energy of the gas: U_{gas, KE}.

(4) 4

Kinetic energy has a measurable rotational part which is relevant with many systems. (We have placed a strike-out on this term not because it is always zero but because rotational kinetic energy will be considered no further in this writing).

In a similar though more abstract manner gas particle potential energies can be divided into extrinsic, "center of mass," and internal components. In conclusion the energy of a gas is written.

(5) 5

What has been argued for a gas, applies as well for a liquid or solid. With this advancement of perspective an increment of system energy can be written:

(6) 6

Thus internal energy and the synonymous idea, intrinsic energy are added to our energy equation. New manners of work are needed to describe fluid or gas behavior. Compression work is an energy transfer mechanism of all substances.