Friday, August 31, 2018

The Simplest Green Plate Effect

Sometime ago Eli created a simple example of how the presence of a colder body can limit the rate at which a warmer one emits energy.  If the warmer body is receiving energy at a constant rate, then the steady state (colliquially equilibrium) temperature of the warmer body will be higher.

Of course this kind of kicks in the nuts arguments about how Uncle Clausius Bunny (he was a Bunny, not a Rabett) said that it was unpossible, even though he said no such thing and was quite aware that warmer and colder objects interchange thermal energy, aka heat, just that more flows from the hotter to the colder so on net, the warmer heats the colder.

Following Izen's lead and a suggestion by Christian Anders, Eli has a stripped down version to break even more heads.

Let's start with a blue plate special and a heat source which constantly transfers an amount of heat a per unit area to the plate.  To maintain a constant temperature the plate then radiates an amount of heat b from each side (yeah, Eli is assuming an really large blue plate, but edge effects are a bitch and if the plate is big enough the heat transfer from the edges can be neglected).  The algebra is trivial and the result is that the blue plate sheds an equal amount of heat in either direction

Now let us insert a green plate behind the blue plate.  Working the example through the bunny at the back of the class with his hand up finds that more of the absorbed heat a is radiated from the blue plate b'=2/3a and c=1/3a since a has to equal b'+c

Eli can keep on adding plates, Ms. Rabett has gone out to buy some extras.  Here is the red plate special.  If somebunny works it through they will find that b'=3/4 a, go another plate and, as Christian pointed out, now b' has increased to 4/5 a and so on. 

Eli has not said anything about how the heat is being transferred, radiation, convection or conduction but since heat transfer, no matter the mechanism, is always proportional to temperature, the temperature of the blue plate must increase as more plates are added.


Fernando Leanme said...

Ebenezer Rabbet figured this out for the case for fur coats: The thicker the fur, the warmer the wearer. He used it in a marketing blitz to convince the 21st Paris Fashion Show attendants to wear grizzly fur coats instead of bunny fur coats.

cit izen said...

I shall have to direct 'nickreality65' here who is at present not only telling me that back radiation does not exist, but that;
"Observed trends don’t exist and/or don’t matter, various observed correlations are not cause."
But I suspect if he denies any warming effect he is a lost cause...

EliRabett said...

He will really appreciate the next post

Bring him on it is getting dull around here.

Christian Anders said...

Thank you for having me.

I'm wondering a bit, why all the deniers are not showing up here?
It's as easy as you demonstrated: You can simply count heat transfer processes, and no matter what's their nature, you will find that in the end you can reach the temperature of the original heat source ( sun or whatever ) as a limit. Not more.

That's exactly the limit claimed by the 2nd law, if you think it through. That's exactly what's our atmosphere provides as a complex cascade of different heat transfer processes. Adding some IR active component shifts the limit up. So simple.

I'm missing the deniers and how they explain why this is wrong. Can't they do it when photons are missing?

Now, different story: I installed to LED lights on an aquarium I own. I could touch them when active, not very warm. I installed reflectors surrounding them, to have more light directed to the water. LEDs are still touchable, but clearly warmer now than without reflectors. Why? Can any pysicist tell me? Maybe a GHE denier?

EliRabett said...