Department of Entropy, from S. Harris

### Eddie Sez:

William Thomson, 1st Baron Kelvin was an Irish mathatical physiscist 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 disovering 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.

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, physiscist, 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.

### 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 closed system has a certain amount of energy in it and that energy can be in various forms such as heat, pressure, or chemical potential. A drop of jet fuel, for example, has chemical potential.

### The Principal of Conservation of Energy

#### Energy can be transfered from one form to another, but cannot be destroyed or created.

The closed system can absorb energy — say the drop of water is heated, or can give up energy — say the drop of water heats something else up. But the energy either came from someplace or went someplace. It wasn't created or didn't disappear.

Back to our drop of jet fuel: sitting in the fuel tank it has chemical potential. Once ignited in the burner can of your engine, that energy is converted to the work done on the engine propelling it forward and to the heat thrown out the tail pipe. All of the energy is accounted for, even if you don't reap all of the benefit.

So how about an example? Here is a typical air conditioning pack from a Gulfstream G450. The pack itself requires no electrical power and does not have any refrigerant, yet it turns 400°F bleed air into 35° conditioned air. How does it do this?

Figure: Air conditioning pack thermodynamics, from Eddie's notes.

There are two inputs: hot engine bleed air and cold ram air. The engine bleed air has thermal energy (it is very hot) and kinetic energy (it is being thrown at the pack with a lot of pressure). The ram air also has significantly less thermal energy (it is relatively colder) and kinetic energy (the pressure is much lower).

The pack has two heat exchangers which are little more than radiators which raise the temperature of the colder air and lower the temperature of the hotter air. The result is the bleed air loses energy while the ram air gains energy.

The pack also has an air compressor. The air enters the compressor at a given energy in the form of heat and pressure. The compressor exerts work on the air and that work becomes heat. (Remember it cannot be destroyed so it must transform itself into heat.) Why raise the heat only to cool it again? Two reasons:

• The heat exchanger works best when the difference in temperatures is greatest. It will subtract more energy from air that is much hotter than air that is only slightly hotter.

• The compressor is connected to a turbine that converts the bleed air's kinetic energy into the mechanical energy required to spin the compressor. The reduction in kinetic energy is greater than the increase in thermal energy so the net effect is less energy in the resulting conditioned air.

There is another player involved: the pack itself. The kinetic energy of the bleed air drives a turbine which spins a compressor and a ram air fan. That kinetic energy subtracts kinetic and thermal energy from the bleed air. The pack also has inefficiencies to consider. The bearings generate heat and the enclosure itself becomes warmer. Both of those subtract energy from the bleed air.

The last stage of the air conditioning pack allows the air to expand. Just as compressing a gas causes it to heat, expanding a gas causes it to cool. The gas expends energy when it expands and that energy comes from the stored heat.

So once you've subtracted all the mechanical, thermal, and pressure energies you end up with cooler conditioned air.

### 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 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 impoossible 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.)