The Gas Constant As The Global Thermostat

Abstract.

The radiative theory of atmospheric gases holds that the temperature of Earth’s surface is higher than it should be according to the Stefan Boltzmann Constant:

http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_constant

To deal with that it is proposed that radiatively active gases in the atmosphere cause that uplift in temperature by radiating outgoing energy back to the surface for a reduction of the rate of cooling which then causes a surface temperature enhancement.

On the other hand we have the mechanical process of lifting the atmospheric gas molecules off the ground and thereafter maintaining atmospheric height. That is governed by the Gas Laws and the energy needed in order to maintain atmospheric height also requires a surface temperature enhancement.

Obviously both processes cannot be duplicating the same effect.

This essay endeavours to sort out that inconsistency.

Surface radiative equilibrium.

I think that can be dealt with very simply.

Once the enhancement of the surface temperature required to mechanically maintain atmospheric height is deducted from the observed surface temperature then the surface can be seen to be at the temperature predicted by the Stefan Boltzmann Constant.

Any need for additional downward radiative energy flow then becomes redundant.

In fact if there were any then in that case the S-B equation really would be breached and the atmosphere would be lost due to a permanent radiative energy imbalance at the surface.

We need to examine the Gas Laws in some detail to consider how the radiative absorption capabilities of Greenhouse Gases could be dealt with given that the Gas Laws have no term for the radiative capabilities of molecules.

The Gas Laws.

The Gas Law for non-Ideal Gases is as follows:

PV = mRspecificT

Where P = Surface pressure, V = atmospheric volume, m is the amount of mass in the atmosphere, Rspecific is the gas constant for the particular mix of atmospheric gases and T is surface Temperature.

Note that it is all about mass with no term for radiative absorption capabilities.

Rspecific is based on the universal gas constant at a given strength of gravitational field and it can vary according to the molecular weight of the particular mix of gases involved.

It comprises a number for the amount of energy required for the necessary work done (in Joules) to lift 1 kg of mass in a gas to a height at which it can become 1 degree kelvin cooler due to the decrease in density with height.

The volume of the atmosphere will therefore vary depending on the average molecular weight of the atmosphere but again that is all about mass.

It must be all about mass because gravity only works on mass. It does no work on radiative capabilities.

Maintaining atmospheric height.

The molecules of an atmosphere are initially raised off the surface by kinetic energy (heat) at the surface. As the atmosphere forms, kinetic energy is transferred from the surface to the gases by conduction and then rises by convection and in rising converts kinetic energy to potential energy. The latter is not heat so the higher the molecules rise the cooler they get due to the lapse rate set by gravity which determines how quickly density can decrease with height.

Once the atmosphere is in place the height has to be maintained by a constant exchange of energy between surface and atmosphere in a perpetual cycle. Adiabatic uplift and descent does that job via uneven conduction from the surface causing density differentials which then give rise to the necessary convection.

The surface therefore has to carry out two separate activities in parallel.

It has to keep supplying the kinetic energy required to maintain atmospheric height and it has to still be warm enough to match outgoing radiation with incoming radiation from an external source.

Only if it can precisely fulfil both functions long term can the atmosphere be maintained.

That is why the Earth’s surface temperature is about 33K warmer than that predicted from the S-B equation and it is all about mass alone.

The thermostatic effect of the Gas Constant.

Within our atmosphere surface pressure is fixed as is total mass and after adjusting for the molecular weight of the constituent gases Rspecific is fixed too.

That only leaves T and V to vary and according to radiative physics V cannot vary without first varying T which is where concern about the warming effects of GHGs comes from.

However, since T and V are on opposite sides of the equation the gas constant serves to regulate their relationship when it comes to the behaviour of gases within an atmosphere.

We all know that expanding a gas causes it to cool by the conversion of kinetic energy to potential energy. Likewise, lifting a gas against the force of gravity will force it to cool.

The gas constant therefore sets the volume of atmosphere needed to leave the surface temperature at the level required to both support the atmosphere AND achieve radiative balance at the top of the atmosphere.

If anything not dealt with by the Gas Laws seeks to alter surface temperature so as to upset system balance then the gas constant immediately alters V in order to stabilise T.

Likewise if anything not dealt with by the Gas Laws seeks to alter atmospheric volume then the gas constant immediately alters T to stabilise V

That applies to the radiative absorption capabilities of GHGs.

If the surface tries to become too warm the volume of the atmosphere rises to restore thermal balance and if the surface tries to become too cool then the volume decreases to restore thermal balance.

It cannot be any other way otherwise those other factors would alter surface temperature so that there would be a permanent imbalance and over time the atmosphere would be lost.

No energy is lost or gained as a result of a volume decrease or increase.  The energy change that had the potential to destabilise the system all gets converted to or from potential energy by the increase or decrease in volume.

In effect, the gas constant puts a fixed figure on the energy that can be held in kinetic form for a given amount of atmospheric mass, a given strength of gravitational field and a given level of energy supplied from outside.

Once that amount is achieved the kinetic energy of the system reaches its optimal level for system stability and all further changes in kinetic energy go to atmospheric volume alone.

The situation is similar to the boiling of water. Once the water is at 100C it can get no hotter. All that happens is a change of volume in the form of steam instead.

So it is with planetary atmospheres.

The broader application.

The principle applies to all factors (other than mass, gravity or insolation variations) that seek to destabilise the system.

Whether there be radiative gases, biosphere changes, volcanic events, ocean cycles, solar cycles, albedo variations or asteroid strikes the same mechanism restores balance over time.

The necessary change being in atmospheric volume it is clear that circulation changes will occur and that leads to my ideas about climate change that I have already set out extensively.

The consequent circulatory changes alter the rate of non radiative energy flow through the system to neutralise the thermal effect of whatever forcing element was trying to destabilise the system in the first place.

Therefore, climate change is the negative system response whereby changes in circulation within an increased or decreased atmospheric volume effectively prevent changes in surface temperature.

On that basis our CO2 emissions would give rise to circulation changes affecting regional and local climates but not average global surface temperatures and the scale of their effect would be insignificant since our emissions comprise such a small portion of atmospheric mass which is the primary determinant of surface temperature.

Additionally we also see large climate changes from natural solar and oceanic variations which overwhelm anything that human emissions could cause.

Adapting the Gas Law for planetary atmospheres.

The usual form, PV = mRspecificT applies to a parcel of gas within an existing atmosphere. Gravitational potential energy can be ignored because such a parcel expands equally up and down. The intermolecular forces are small enough to ignore.

For a planetary atmosphere as a whole that is not good enough because gravitational potential energy is very close to 50% of the energy in an atmosphere.

We need to find an equation that allows factors other than mass, gravity and insolation to affect V without affecting T because according to the Gas Laws T is determined only by the amount of KE needed to keep the mass of the atmosphere off the surface at a given height over and above that required for top of atmosphere radiative balance.

I suggest the following variant:

PV = mRspecificE

Where E represents total atmosphere energy content (KE + PE) and the value of Rspecific determines how much of E can be in kinetic form (KE) as heat and how much in potential form (PE) as height.

In that way we can allow factors other than mass, gravity and insolation to affect V without affecting T because T is determined only by the amount of KE needed to keep the mass of the atmosphere off the surface at a given height and in turn that is determined by mass (m) and the individual gas constant for the particular atmospheric composition (Rspecific).

Once one has enough KE to do that job all additional factors influencing total atmospheric energy content must go to PE alone.

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