Is it possible in the real world to find a truly adiabatic process? 

Well, let's begin by re-examining the definition. In theory, if not in practice, the idea of an adiabatic process is fairly straightforward. It's a system, usually a body of gas, that either does work or has work done on it, without any transfer of heat to or from its immediate environment.

According to the first law of thermodynamics:

\(Q = ΔU + W\)

where \(Q\) is the flow of heat in or out of the system, \(U\) is the internal energy of the system, and \(W\) is the work done on or by the system. Now, in an adiabatic process, \(Q = 0\), hence:

\(ΔU = -W\)

Therefore, because the internal energy of a gas depends only on its temperature, any change to \(U\) will depend on whether work was done on or by the gas. For example, work done by the gas will entail expansion, an increase in its volume, which results in a lowering of its temperature and, consequently, its internal energy.

Another useful equation with particular regard to ideal gases, is as follows:

\(pV^γ = \text{constant}\)

where \(p\) is the pressure of a gas, \(V\) is its volume, and \(γ\) is the adiabatic index - the ratio of molar heat capacities of the gas at constant pressure and volume, respectively. \(γ\) depends on the molecular structure of the gas particles and is pertinent since extra work is required to increase the temperature and hence average translational kinetic energy of a gas whose constituent particles have more than three degrees of freedom. For example, a diatomic gas with \(γ = {7\over5}\) has more energy sinks (vibrational, rotational, etc), than a monatomic gas with \(γ = {5\over3}\). Therefore, any increase of internal energy resulting from work done to the system needs to be shared across the extra degrees of freedom before the translational energy, the pressure dependent component of each particle, increases.

So, before going back to the question at the top of the piece, what are the conditions required for a real world adiabatic process to take place? Certainly, the system will need to be well insulated in order to prevent heat gain or loss to or from the surrounding environment. Any adiabatic process needs to proceed sufficiently rapidly that there isn't time for any significant heat loss or gain to or from the surroundings, and there will ideally be minimal temperature difference to the immediate environment. In a closed system it is important that any collisions between the constituent particles of the system and its walls are elastic.

Of course, in the real world the above conditions are probably going to be at best approximated. A full understanding of adiabatic processes is important, as we are better able to design systems where inevitable loss of energy to the surroundings is minimised, and the more efficient, cost effective and environmentally friendly they will be. Comparisons between theoretical and “actual” \(pV\) indicator diagrams of cyclic engines, for example, can help engineers understand where energy is being lost, due to friction, fuel burning efficiency, valve inefficiency, and so on. 

Examples of real world adiabatic processes are the compression (heating) and expansion (power) strokes of the pistons in an internal combustion engine. Comparable, somewhat simpler, examples are the effects of the heating of the air in a bicycle pump as it is quickly compressed; the sudden reduction of the volume of air in the pump causing a commensurate increase in its internal energy. And, similarly, blowing through pursed lips, as if whistling, onto your hand, will cool your skin due to the sudden increase of volume of the body of air as it leaves your mouth. Conversely, breathing on your hand with an open mouth entails no change of volume and hence the air feels warm. Similar effects are also present in the working of gas turbines, refrigerators and heat pumps, as gas is conversely compressed or passed through expansion valves.

Popping the cork or releasing the cap on a bottle of fizzy drink causes a sudden adiabatic increase in volume of the air between the liquid and the bottle top, resulting in an often visible cloud of vapour, as it suddenly cools and condenses. Adiabatic processes can even be present in the atmosphere, for example as clouds form when a cooling mass of air is forced over a range of hills or is carried upwards by an ascending convection cell.

To some degree, even the alternating compression and rarefaction of a gas due to sound waves can cause adiabatic heating and cooling. Adiabatic processes are common in astrophysics, particularly with regard to the expanding and contracting cores and envelopes of stars, leading at extremes to both star formation as molecular clouds contract, and spectacularly to supernovae explosions at the end of the lives of particularly massive stars. One could even surmise that the cooling of the entire Universe due to its expansion is an adiabatic process! 

So, at the end of the day, are there any truly one hundred percent real world adiabatic processes? Well, with the right conditions, approximately adiabatic processes are more common than you might at first consider. Ultimately, though, there's just no way of getting around the second law of thermodynamics, according to which, “there's basically no such thing as a free lunch!”.

Images

• D. Napier & Son Ltd, 'Aero Engine in the Making', England, circa 1918 photo by Museums Victoria on Unsplash
• Inflating bike tyres using a pump photo by Alextredz, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons