Lies, Damned Lies and Statistical Mechanics – 5
Reading standard physics texts one could be forgiven for
believing pressure is a simple physical property. You heat something in a
container and the pressure rises. Cool it and the pressure reduces. Similarly
for changing the volume, such as by pushing in or pulling out a piston. The
pressure described there is thermal pressure due to the kinetic interactions
between the molecules in the substance.
There is another form of pressure we experience on Earth: atmospheric
pressure is actually, in effect, the weight of the atmosphere. Oceanic pressure
is similar, being the weight of the atmosphere plus the weight of the water. Another unhelpful feature is that “pressure” can mean the
force per unit area impinging on a body immersed in a fluid or some applied
force that results in the former or the effective momentum of a moving body of
fluid.
In space there are no
containers. Thermal pressure tends to dissipate by expanding the gas until
its pressure matches that of its surroundings. Where pressure exists in astrophysical
objects it is caused mainly by gravity, in the same way as atmospheric and
oceanic pressure here on Earth. Gravity, of course, tends to be somewhat higher
(than on Earth) around stars and major planets. From this one can appreciate
that stability occurs when the pressures balance. In laboratory experiments
thermal pressure is balanced by inward pressure provided by the container, but
this tends to go unnoticed. To make sense of this, I refer to inward pressures,
like gravity and our background container, as impressure and pressures that
push outwards, like thermal pressure, I call expressures. (Think of implode and
explode.) Mathematically, expressure is positive while impressure is negative.
We now have a rule: in a stable fluid impressure equals
expressure. Or, mathematically, impressure+ expressure=0.
There are other pressures.
Electron degeneracy
pressure is a force between atoms borne of the Pauli Exclusion Principle
and depends on the number density of electrons and the electron energies.
Again, it is not something we directly experience in daily life, but it is
omnipresent and, for example, contributes to the sensation of a solid object. In
a star this expressure can be very high due to the high density, under
gravitational pressure.
Radiation pressure,
almost undetectable here in daily life, occurs when electromagnetic radiation
impacts atoms and raises the energies of the latter. It tends to push the atoms
away from the radiation source. It can therefore act as expressure in a star’s
corona or as impressure in the case of stellar radiation affecting a nearby planet’s
atmosphere. This pressure is dependent on the radiation flux, the atom density
(the number of atoms per cubic metre) and other factors such as the probability
of a photon colliding with an electron (which is where quantum mechanics come
in). Near an intense source of radiation, such as a star, this pressure can be
enormous. In the solar corona, it is largely radiation pressure that stops the
corona collapsing under its own weight.
There are also electrostatic pressures affecting charged
gases, and let’s not forget inter-atomic gravity, small though it is.
In a star, the pressure balancing act entails the
combination of electron degeneracy, radiation and heat pitted against
gravitational pressure. Close to the solar surface the density is high so
radiation and electron degeneracy pressures are high and almost match the
weight of the full height of the corona above. If the expressures start to win
the balancing act, the gas/plasma expands, becoming less dense, so the expressures
decrease accordingly and the balance is restored. The solar wind is an extension of the corona and the pressure driving it also reacts backwards adding to the gravitational pressure.
Pretty much the same principle applies to Earth’s
atmosphere. Atmospheric pressure is largely controlled by gravitational
pressure. This results also in control of the mean atmospheric temperature at
sea level. When the air is heated, either by a hot surface or by solar
radiation, it expands upwards (not to be confused with convection, which also
occurs), reducing its density and thermal pressure until the latter balances gravitational
pressure. Radiation (outwards) and electron degeneracy pressures play little if
any part in Earth’s atmospheric environment. Solar radiation reaching Earth
causes radiation pressure towards the surface of the planet so acts to assist
gravity. Since air density is greatest close to the surface, this is where
solar radiation pressure is highest. So air pressure is a function not just of heating but also of gravity.
I wonder if
meteorologists take gravitational pressure into account in their (rather complicated) calculations:
I suspect not.
Observation: the combined effect of these pressures is that
kinetic temperature in a gaseous region, not constrained by a container, is inversely
proportional to the density, as is evident in the solar corona and
inter-stellar gas clouds. The gas law
does allow for this, but, in containers pressure rises with temperature so this
effect is not normally seen. The behaviours of planetary atmospheres are far too complex
to show this property.
The upshot of all the above is that any analysis of pressure in
a fluid must be undertaken with due regard to the combination of different
types of pressure present in the environment under examination and not to make
premature assumptions based on relatively simplistic laboratory measurements. Otherwise we haven’t moved on from the nineteenth century.