1. Jul 11, 2009

### Kibuzo

Disclaimer: English is not my native language. I'll try to do my best, but i could put some inappropriate term somewhere, if so please forgive me and feel free to correct me, the more i learn the best :P

Hello guys.
I'm new here, but i don't really think that this post could be addressed to "homework question", if so please forgive me and move my topic.
The only "homework-related" thing is that i heard this question in an exam, and i really don't know how could i answer completely to this question. Also, it would really seem lame to get to the teacher telling him "hey, could you tell me how should i answer you to this question, just in case you ask me", SO LAME! :P

Now, let's get to the core of the matter
The thing is: how can i show that the atmosphere is adiabatic? (the question was "tell me about the adiabatic atmosphere")
I've put myself in front of a pen and a paper and i started thinking. First of all i wondered that the fact that every adiabatic is also isoentropic could have helped me, and i told myself that the isoentropic way could have been easier.
But it probably wasn't, i tried to show that the heat transferred to the atmosphere in some way would have increased its entropy for as much as it would have been lowered at the time in which the heat would have been released, but it definitely was not the thing, the atmosphere changes its temperature very often, depending on the altitude, the time of day etc, also there are many different sources of heat and i really couldn't tell where could the heat have gone after i release it into the air.
Then i started thinking differently. I thought of a bubble of air lifting up, its volume would increase (like with helium baloons that suddenly explode at higher altitude) and it would have probably followed the law $$PV^{\gamma -1} = constant$$.
I thought about the water that evaporates and then condensates, the same ammount of heat transferred to the water to let it evaporate would still be in the atmosphere under the form of latent heat that would have been released when the water rains again. Sto still no heat change in the atmosphere.
This two are proably not enough to cover an exam question, but what else could i add?

Also, i thought of the things in a bigger scale. There is the earth with inside some lava and many other hot crap that spits up is heat. On the other side we have the sun that spits down its heat. In the middle our atmosphere seems to absorb everything, but it is also clear that we don't live in a flaming sphere (well, not that clear in this part of the year, but... well), so the atmosphere is supposed to release its energy somewhere in some way.
But if we assume that there is the void in outer space, how can it cool down the earth's temperature, what is its specific heat?
And if it is not for thermal contact with the outer space how else does the atmosphere loose all the heat gained from the sun and from the depths of the earth?

The level of the question is of classic physics in a physics degree course, first year (it could not be clear, it is never clear when i hear of american courses...)

Thank you for the answers, and congratulations for the forum!

2. Jul 12, 2009

### Andrew Mason

First of all, heat flows into and out of the atmosphere all the time. Heat from the sun heats the earth and some of this heat flows into the atmosphere. So as a whole, it is not adiabatic. It is not in a state of thermodynamic equilibrium either.

However, a column of static air will have adiabatic characteristics in that the adiabatic condition applies throughout the column: $PV^\gamma = K$. I think your question relates to that: Why does the adiabatic condition apply to a column of air?

AM

3. Jul 12, 2009

### Kibuzo

Be it, the global part about heat flowing from everywhere has been cut out, good :P.

I still need to know what you also said: "why does the adiabatic condition apply to a column of air"?. I mean there are 3 ways of thinking about an adiabatic: $$PV^{\gamma}=k$$, net heat flux=0 or no variation of entropy.
I can suppose that the column of air is in equilibrium in every point, otherwise it would change as long as we don't get to the static condition of maximum of entropy, so the entropy of every point is at its maximum. Now, what is the point of the adiabatic column of air? does it mean that when i go up and down through it i get no heat gain/loss and that the whole column is isoentropic? And how can i show it? do you have any demonstration?

thank you for answering by the way!

Last edited: Jul 12, 2009