Sunday, 26 July 2020

Eunice Foote - 19th century Climatologist

From Wikipedia

Foote conducted a series of experiments that demonstrated the interactions of the sun's rays on different gases. She used an air pump, four mercury thermometers, and two glass cylinders...

Her own two-page write is up here.

1. She pumped air out of one container into the other and left them in the sun for a while. Result:

Decompressed air - 88 F
Compressed air - 110 F.

"This circumstance must affect the power of the sun's rays in different places, and contribute to produce their feeble action on the summits of lofty mountains."

Yes, that is a large part of the actual explanation for sea-level temperatures, which is the gravity-induced lapse rate. Also, common sense tells us, it is pretty hard to heat up a vacuum (there is nothing to heat up), so decompressed air must heat up less.

2. She filled one container with moist air and one with dried air and left them in the sun for a while. Result:

Dry air - 108 F
Moist air - 120 F

I'm not sure what to make of this, but in itself. The specific heat capacity of moist air is higher than for dry air, so this doesn't follow the pattern observed in 3. below. But this is pretty irrelevant in climate terms. What makes a big difference in real life is the latent heat of evaporation (which cools the surface) and the corresponding latent heat of condensation (which warms the air) and thus reduces the lapse rate and overall Greenhouse Effect (by about one-third). It would have been more realistic to have a container filled half with water and half with dry air.

3. She filled the containers with different gases and left them in the sun for a while. Result:

Hydrogen - 104 F
Common air - 106 F
Oxygen - 108 F
CO2 - 125 F

Well, yes, of course. What are the specific heat capacities of those gases (in the 275 - 300 K range)?

Hydrogen - 14,025 J/kg/K
Common Air - 1,006 J/kg/K (or possibly 1,014 J/kg/K)
Oxygen - 916 J/kg/K
CO2 - 832 J/kg/K

Rather unsurprisingly, her experiment shows that things which require less energy to warm up, warm up the most. As ever, 'back radiation' has nothing to do with it. We'd have to adjust this for the mass of the gas compared to the mass of the glass containers and the specific heat capacity of glass (assuming they warmed to the same temperature), but the overall picture is clear enough.

She goes off on a bit of a tangent: "An atmosphere of [CO2] would give to our earth a high temperature; and if as some suppose, at one period of its history the air had mixed with it a larger proportion than at present, an increased temperature from its own action as well as from increased weight must necessarily have resulted"

She is correct, but has the logic and magnitude wrong.

A lower specific heat capacity means a higher lapse rate. If our atmosphere were 100% CO2, the lapse rate would be approx. 2K/km higher (assuming relative humidity stays the same). The average temperature of the atmosphere can't increase as it is dictated by solar radiation. The average temperature is found half way up (approx. 5 km), so sea level temperatures would increase by approx. 10 K, and the temperature at the top of "lofty mountains" above 5 km altitude would fall.

But we would all have suffocated long before then.

In real life, we know that CO2 concentrations are likely to rise from pre-industrial 280 ppm to over 500 ppm this century, and quite possibly to over 600 ppm in the next.

If anybody can be bothered to work out the new average specific heat capacity of air will be when CO2 is 0.05% or 0.06% instead 0.028%, and then work out the new lapse rate (making some heroic assumptions as to whether and how much relative humidity would increase and moderate this) and the resulting impact on sea-level temperatures, then knock yourself out. Most calculators won't have enough decimal places to give a meaningful answer, and even if it does, the additional sea-level temperature will be within the margin of error of even the most accurate thermometers.


From this experiment, she stated “The receiver containing [CO2] became itself much heated — very sensibly more so than the other — and on being removed [from the Sun], it was many times as long in cooling.”

As a general rule, gases with a lower specific heat capacity are better insulators and cool down more slowly, so that's hardly surprising either.


View from the Solent said...

re moist air
The specific heat of water is very high - ~4000J/kg K at everyday temperatures.
Doesn't take much moisture to outstrip CO2.

Mark Wadsworth said...

VFTS, yes, specific heat capacity of water vapour is 1,900 J/kg/K, nearly twice as much as for dry air, so we would expect s.h.c of moist air to be higher than dry air.

So, for a given amount of energy, moist air should warm LESS than dry air. But she said it warmed MORE.

View from the Solent said...

Sorry, misread the numbers.
I *think* that the infrared absorption coefficient is at least as important as specific heat. If the coefficient is high enough then the more efficient heat absorption would counteract the higher specific heat.
Can't easily find the relevant data for comparisons.

Mark Wadsworth said...

VFTS, if you can find that out and see how much of her results it explains, that would be most helpful.

View from the Solent said...

OK, I'll have a dig around when I can.

Graeme said...

Warming, cooling it's always bad news

They always seem to be making this stuff up as they go along. There is no proper hypothesis that they are testing, no sense of how new evidence fits into the framework. If CO2 warms the atmosphere lower down how can it cool the atmosphere further up?

Mark Wadsworth said...

G, "If CO2 warms the atmosphere lower down how can it cool the atmosphere further up?"

That is one of the few bits that actually makes sense (at least superficially).

If CO2 acts like insulation, it keeps sea level warmer and the upper layers cooler. Like loft insulation keeps your home warmer and keeps the loft cooler.

Clearly, the overall average temperature of the surface and the atmosphere is dictated by the sun. Like the overall average temperature of home plus loft is dictated by your central heating.

(I'm drafting a post on why it still makes no difference to sea level temperatures, it's a maths thing).