William Thomson, 1st Baron Kelvin was an Irish mathematical physicist and engineer who died right around the time the Wright Brothers were first using the compressibility of air to temporarily escape the pull of gravity. Kelvin, besides discovering where absolute zero is — at 0° Kelvin of course, was also the first to postulate the field of thermodynamics, henceforth dooming engineering students to the first of many "make it or break it" courses on the way to their degrees.

— James Albright

#### Updated:

2013-09-26

Lord Kelvin

So what's all this mean to a pilot? Lots. Thermodynamics is what allows a jet engine to turn fuel into thrust. It also rules the roost in your air conditioning and pressurization systems. You don't need all those formulas and fancy theorems, but it does help to understand why gases behave they way they do if you ever need to trouble shoot that jet engine or air conditioning pack of yours.

Oh yes, most of this comes from my notes from three thermodynamics courses at Purdue and my failing memory. If you are a mechanical engineer, physicist, or thermodynamics professor, I would be happy to cite you as a reference if you can explain it better for a pilot audience. Oh yes, you are wondering why I took three thermodynamics courses? Well, there was basic, advanced, and advanced the second time around. This stuff can be difficult.

1 — The "First Law of Thermodynamics"

2 — The "Principal of Conservation of Energy"

3 — The "Second Law of Thermodynamics"

4 — "Energy-Maneuverability Theory"

5 — The "Third Law of Thermodynamics"

## 1

#### The "First Law of Thermodynamics"

The increase in internal energy of a closed system is equal to the difference of the heat supplied to the system and the work done by it.

A closed system is anything you want it to be, say a jet engine or an entire airplane, but it is easier to understand the theory if you consider something smaller. A drop of water, for example. The water itself has an amount of stored energy in terms of its temperature. If you were to place the drop onto a colder surface, the drop will tend to raise the temperature of the cold surface, increasing its stored energy while lowering its own. The warm water does work on the cold surface by releasing its stored energy. We call this stored energy "potential energy" and the transfer of energy is work.

There are other forms of potential energy, such as that found stored in jet fuel, which is chemical energy. That stored energy is released when the conditions are right to ignite the fuel.

## 2

#### The "Principle of Conservation of Energy"

The increase in internal energy of a closed system is equal to the difference of the heat supplied to the system and the work done by it.

A closed system is anything you want it to be, say a jet engine or an entire airplane, but it is easier to understand the theory if you consider something smaller. A drop of water, for example. The water itself has an amount of stored energy in terms of its temperature. If you were to place the drop onto a colder surface, the drop will tend to raise the temperature of the cold surface, increasing its stored energy while lowering its own. The warm water does work on the cold surface by releasing its stored energy. We call this stored energy "potential energy" and the transfer of energy is work.

There are other forms of potential energy, such as that found stored in jet fuel, which is chemical energy. That stored energy is released when the conditions are right to ignite the fuel.

## 3

#### The "Second Law of Thermodynamics"

Heat cannot spontaneously flow from a colder location to a hotter location.

Kinetic and potential energy dissipate. Over time, temperature, pressure, and chemical potential tend to even out. This process is known as entropy and is often stated thusly: things go from order to disorder.

The second law is unique to thermo and puts limits on what is physically possible in the conservation of energy. It is called the "law of entropy" and applies to all systems but is most easily introduced by its effects on a closed system — that is, one not acted upon by outside forces. The second law postulates that the expenditure of energy does not ebb and flow. It says that in a closed system, the transfer of heat goes only in one direction, from a high temperature to a low temperature.

Source: Coram, pg. 127

The second law was the first nonreversible law in physics — something almost beyond the pale of science. It says the universe goes from order to disorder. . . . Some even use the second law to try to prove the existence of God. This argument has it that God established order (low entropy), and since then the universe as progressed and continues to progress to disorder (high entropy).

Source: Coram, pg. 128

So what does this mean for us pilots? Charles E. Cooper was a 19 year old majoring in aeronautical engineering when he happened to sit in class next to then Captain John Boyd, the Air Force fighter pilot who almost singlehandedly changed the art of war. Boyd wanted to better understand the second law of thermodynamics:

Cooper began talking about the second law, explaining how more usable energy always goes into a system than goes out, because there is unavailable energy called entropy. All entropy means, Cooper said, is that no system is one hundred percent effective; if it were, you would have a perpetual-motion machine.

Source: Coram, pg. 131

In terms of a fighter pilot's need to out maneuver an adversary, the aircraft has energy in terms of altitude and speed and can add to that energy using the engine's thrust, which converts the chemical energy of fuel. Much of the fuel's energy does not translate into energy for the pilot because it is expended in heat thrown aft or absorbed by engine components.

But let's consider an even simpler idea: an airplane is steady cruise flight with a constant thrust setting. If the pilot pushes the nose over to descend the aircraft will necessarily pick up speed. If the pilot levels momentarily and then climbs back to the original altitude, the aircraft will end up at a lower speed unless enough fuel was burned to increase the thrust to weight. Why is that? It is because an amount of speed (energy) was consumed by the g-load needed to level off at the bottom of the descent and then to begin a climb. And that leads us to Boyd's:

## 4

#### "Energy-Maneuverability Theory"

In an equation, specific energy is denoted by "PS," (pronounced "p sub s"). The state of any aircraft in any flight regime can be defined with Boyd's simple equation:

$PS = ( T - D W ) V$

or thrust minus drag over weight, multiplied by velocity. This is the core of E-M.

Source: Coram, pg. 147

This elegant equation explains much of what you might intuitively know about flying airplanes:

• At any given moment, you can increase speed by increasing thrust, decreasing drag or weight
• You can also decrease speed by decreasing thrust or increasing drag (and those of us who could air refuel, by increasing weight)
• You can also change speed by changing the specific energy, PS, by trading altitude (up or down), which trades potential energy (altitude) for kinetic energy (velocity).

## 5

#### The "Third Law of Thermodynamics"

As a system approaches absolute zero the entropy of the system approaches a minimum value.

While not really germane to us pilots, this law just tells us it is impossible to get to absolute zero or to the point where the energy of everything has completely scattered so it is all at the minimum value. (It can approach the value, it cannot reach it.)

#### References

(Source material)

Coram, Robert, Boyd: The Fighter Pilot Who Changed the Art of War, Back Bay Books, New York, NY, 2002