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#### Charmed

**From Units Sold to Car Dealership Temperature**

Dear All:

In the attached, I have continued the analysis of the car dealership problem and show how to derive the notion of car dealership temperature T, following the logic used by both Planck (in 1900) and Einstein (in 1905) when they developed quantum physics. Einstein uses a simplified version of Planck's radiation formula to arrive at the idea that light must be composed of particles having the elementary energy quantum hf. However, it is worth recalling Einstein's exact remarks. Einstein shows that

*as far as its entropy is concerned, light can be thought of*as being made up of particles having an energy hf.

As far as its entropy is concerned. Einstein also shows that the temperature T of light, or electromagnetic radiation, must be given by T = U/S where U is the energy and S the entropy. He imagines light, or electromagnetic radiation to have a certain energy density and a certain entropy density, just like Newton starts with the idea of density when he defines what he means by mass in physics. The total energy is the energy density times the volume enclosed by the light front. The total entropy is the entropy density times the volume. The ratio of energy to entropy is the temperature. Since entropy tends to a maximum, the temperature will tend to a minimum. And, so on.

Now, we can use the same arguments, generalize them and arrive at the idea of temperature, from the units sold by the car dealership. Each unit sold has the attribute of money, which is analogous to energy. The missing notionsof entropy and temperature follow using the arguments of Planck and Einstein.

The graph in Figure 6 (updated Microsoft PowerPoint file) shows how the average price per unit M increases as the temperature T increases. However, we must deal a constant k, which is analogous to the Boltzmann constant, which includes the concept of mass, or moles of a substance. Likewise, there is "mass" in the business world. How does this come about?

To understand this, we must understand how the business world operates. We can think of it like an engine, see Figure 7 in the attached file. IMHO, together with some of the ideas outlined in the earlier posts, this completes the analogy. The idea of a fixed quantum of profits (or costs) can be deduced from these considerations. The law y = hx + c where x is revenues and y is profits is the exact analog of Einstein's photoelectric law. The statement Profits = (Revenues - Costs) is the analogy of the law of conservation of energy, also called the first law of thermodynamics. The idea of temperature T is implied in the second law and formalized via the zeroth law of thermodynamics. These points are also discussed briefly in the appendices to the attached Word document.

Have a happy holiday season and a great new year.

Charmed