"Heat" as the Currency of Work
(revised May, 2008)
John A. Gowan
home page (page 1)
home page (page 2)
(See also: "Introduction to Entropy" and "Spatial vs Temporal Entropy")
The usual definition of spatio-temporal (mixed, "relative", or "work" entropy) is the energy contained in a closed, material system which in principle is not available for transformation to work. In the typical case this entropy-energy manifests as "waste" heat, "degraded" energy (dQ/T) contained in randomized molecular motion, which, in addition to the enervation occasioned by the disorder of its molecular energy vectors, will eventually be radiated away, irretrievably lost due to "infinite" velocity c and the cosmic expansion of space. The inexorable march of time and the expansion of history is also involved in the entropy loss of any material or mixed entropy transformation, as each moment slips away, never to be repeated or recovered. (See: "Spatial vs Temporal Entropy".)
"Heat" is a most interesting state of energy, the central player in mixed entropy and energy transformations. "Heat" is the randomized kinetic energy of molecular motion, a mixture of free energy and matter, hence involving c, T, and occasionally G (in very large masses such as stars). "Temperature" is a measure of the average velocity (or average kinetic energy) of molecular motion; "heat" is a measure of the number of molecules with a given temperature. "Work" entropy manifests as "heat" (Q) divided by absolute temperature (T), and the lower the temperature (per unit of heat (calories)), the greater the entropy - the less energy available for work or transformation.
All forms of energy can be completely converted to heat, but heat cannot be completely converted into work or other forms of energy because of the entropy heat contains. Heat is said to be a "degraded" form of energy because it contains a lot of entropy in the form of random, disorganized, "self-defeating" (colliding, interfering, opposing) molecular motion. It is easy enough to randomize an energy source or form, but once randomized, energy must be expended to restore any more ordered state. Destruction is easy, construction is difficult.
In order to transform one form of energy into another, we must always pass, at some point in the process, through the entropy domain of heat - the burning of fuel to produce steam power being the prototypical example. A lump of coal has mainly temporal, quiescent, bound-energy entropy until it is burned. Coal has existed quietly for millions of years with its entropy almost entirely in the "pure" temporal form. When coal is ignited, however, we release its potential chemical energy and produce a mixture of free and bound energy (molecules in motion, kinetic energy) and likewise an accompanying mixture of spatial and temporal entropy drives (as gauged by "velocity" c and T). It is this potent mixture of c and T (time) that guarantees a lot of entropy-energy will be irretrievably lost, radiated away second by second, due to the operation of both these "infinite" velocities.
In addition to the escape of radiant energy in space and time, the randomized distribution of molecules and their velocity vectors is crucially important to the entropic function and definition of "heat", because the randomization "degrades" or disorganizes the energy of heat such that only its temperature and quantity remain as significant parameters: no net molecular velocity in any particular direction survives. Hence all sources of heat are alike in this respect - they have lost any "personality" due to the randomization of the velocities of their constituent molecules - a kilocalorie of heat is "anonymous". The most random distribution is not only the most probable, but also the most symmetric, which is a basic connection between entropy and symmetry.
Randomization is the most symmetric, probable, or ground state of maximum entropy (for a given temperature), because it would require energy inputs to "unrandomize" or move to any more ordered, asymmetric, useful, or improbable state: this is the essence of Boltzmann's insight. The randomized component of energy cannot be used to do work - instead, work would be required to order it into any useful configuration (as by "Maxwell's demon"). The randomized component is where the useless energy or entropy resides (in matter), as this energy cannot be transformed to work, it is too busy interfering with itself, canceling out and opposing any useful component of directed energy.
"Heat" is like a universal energy currency or "money" which allows us to buy various goods and services (transformations of energy), but which contains in itself the entropy-interest charged "up front" for our use of the energy currency - which is just why we are forced to use it for these transformations in the first place. "Heat" is thus nature's moneylender, preventing the abuse of energy by charging entropy-interest. Humans transform our own work into the universal social currency of money, an "anonymous" energy form which allows us to buy specific items at the market place; similarly, we must first transform any energy source into heat, liberating its free energy component and activating Boltzmann's entropy of probability, before it can be transformed to work or some other form of energy.