Thoughts on Adiabatic Processes

[Facial]

This took me an embarrassingly long time to come to grips with. I've studied a good deal of physics in high school and college (not majoring in it, but somewhat related - in structural engineering). Until recently, I always thought that the process of adiabatic heating could be thought in terms of elastic collisions, where gas molecules could be simplified into 3 degrees of freedom per molecule, much like billiard balls. When I compress a piston, the translational motion of that piston wall (assuming rigid behavior) adds momentum to these molecules, heating them up.

I've more recently realized that the classical analogy doesn't hold in explaining why certain gases heat up more than others when compressed. Some of the lightest gases, such as hydrogen and helium, even cool during compression in what's known as the Reverse Joule-Thomson effect. These assume processes near room temperature and far from their inversion temperature. And yet such light gases supposedly satisfy the main assumptions behind ideal gas behavior along with its Newtonian mechanics. So, the electromagnetic near-field interactions between gas particles seems more important for light gas molecules - that is, deviations from the ideal gas law - than it would be for heavier gas molecules.

Hydrogen and helium have relatively low inversion temperatures, so a qualitative description of its near-room temperature behavior is that near-field repulsion tends to dominate.

It's an interesting twist in how I always thought about gases (for the last 20+ years of my 36-year life!), but I wonder whether the breakdown in this grade school heuristic extends across diatomic, triatomic, and larger molecules for which behavior is known to be more electrostatically active and moreover attractive, instead of repulsive, near room temperature.

What originally motivated me to think about this was thinking about how heat pumps really work - why they are more efficient for a house than an ideal furnace, i.e., creating heat energy 100% from scratch - without violating conservation of energy.

Comments and thoughts appreciated.

 

[exchemist]

This took me an embarrassingly long time to come to grips with. I've studied a good deal of physics in high school and college (not majoring in it, but somewhat related - in structural engineering). Until recently, I always thought that the process of adiabatic heating could be thought in terms of elastic collisions, where gas molecules could be simplified into 3 degrees of freedom per molecule, much like billiard balls. When I compress a piston, the translational motion of that piston wall (assuming rigid behavior) adds momentum to these molecules, heating them up.

I've more recently realized that the classical analogy doesn't hold in explaining why certain gases heat up more than others when compressed. Some of the lightest gases, such as hydrogen and helium, even cool during compression in what's known as the Reverse Joule-Thomson effect. These assume processes near room temperature and far from their inversion temperature. And yet such light gases supposedly satisfy the main assumptions behind ideal gas behavior along with its Newtonian mechanics. So, the electromagnetic near-field interactions between gas particles seems more important for light gas molecules - that is, deviations from the ideal gas law - than it would be for heavier gas molecules.

Hydrogen and helium have relatively low inversion temperatures, so a qualitative description of its near-room temperature behavior is that near-field repulsion tends to dominate.

It's an interesting twist in how I always thought about gases (for the last 20+ years of my 36-year life!), but I wonder whether the breakdown in this grade school heuristic extends across diatomic, triatomic, and larger molecules for which behavior is known to be more electrostatically active and moreover attractive, instead of repulsive, near room temperature.

What originally motivated me to think about this was thinking about how heat pumps really work - why they are more efficient for a house than an ideal furnace, i.e., creating heat energy 100% from scratch - without violating conservation of energy.

Comments and thoughts appreciated.

Interesting topic. In the case of hydrogen and helium, the van der Waals attraction between the molecules is very small, as reflected in their very low melting and freezing points. (In fact helium has no freezing point at all, as the zero point kinetic energy of the atoms exceeds the binding force available.) So these are close to ideal behaviour, I suppose.

Your choice of terminology to describe van der Waals forces is a bit strange though. The term "near field" is generally applied to EM radiation effects, whereas intermolecular forces are electrostatic in nature. In the absence of permanent dipoles on the molecule, van der Waals forces are another name for London forces. These are due to the polarisability of the molecule whereby, due to the uncertainty principle, instantaneous temporary dipoles arise on one molecule which then induce a dipole in a neighbour, creating an electrostatic attraction.

When molecules collide at high speed though, the electron cloud is distorted by electrostatic repulsion and by the operation of the Pauli Exclusion Principle, which prevents fermions from occupying the same orbital state. This is what causes them to rebound from one another in intermolecular collisions. As hydrogen and helium are the lightest molecules, they have the highest mean molecular speed at a given temperature. So at any instant there is a proportion of them that are in mid-collision, during which kinetic energy has been temporarily converted into electrostatic potential energy. If the gas expands, so that the pressure drops, that proportion becomes less, so there is a net release of potential energy. This, according to my admittedly rather rusty recollection, is the source of the reverse Joule-Kelvin (or Joule-Thomson) effect.

In general, more complex molecules will have greater van der Waals forces between them, due to their greater polarisability, the more so if the molecule also has permanent dipoles. So then you get the simple Joule-Thomson effect, until very high temperatures are reached at which the "compression" of molecules during collisions becomes a dominant factor.

But you don't need any of this to explain why heat pumps are efficient compared to a furnace. That's simple thermodynamics. You are taking low temperature heat from the ground or the air and, by doing mechanical work, you are raising its its temperature. So what you get out as heat for your house is both the input (electrical) work and the heat the device has sucked out of the low temperature source. It's true that the operating cycle of a heat pump makes use of the Joule-Thomson effect, but you can understand the thermodynamics without getting into all that.