Thermal Physics?

Question

Hi looking over my physics notes and they are sketchy at best any help filling in all or some of the gaps would be appreciated.
1) Concerning thermal transmittance through composite walls, why must the heat flow be the same through each section of wall?
2) Molar heat capacity at constant volume = dU/dT this seemed to appear at random not sure what U refers to at all? pe? any ideas
3)on the exponential atmosphere
I have the formula p(h)=p[h=0].exp(-mgh/kT) then i have kT/mg=h[0]=8041 at 273. Unsure how you get to this from the formula and no idea where 8041comes from (could it be a given value? was under the impression h[0] was sea level though). desperate for help on this one
4)Is decreasing air pressure with increased height down to lack of high mass molecules or less air above you or a combination of both?
5) Finally a bit of a long shot but on intermolecular potential I have that notation that F is 2nd derivative of U w.r.t r evaluated at a. then written next to it (r-a)?

Answer 1

1. This only applies in a steady state situation, that is when the temperature does not change over time.

If the heat flow out of one section is different than the heat flowing into an adjacent section, then there will be a temperature change at the interface because there is a net transfer of thermal energy into or out of it. This violates our assumption of a steady-state situation.

2. U is energy.

3. You're missing two things: units that go with the 8041 figure, and the value of the mass m.

IF we use the average mass of an air molecule, (28.8 atomic mass units), then we get 8041 METERS. This is the height at which the pressure is 1/e = 0.367... as much as it is at h=0. For temperatures other than 273 K, it will be something other than 8041 meters. ***

It appears that the "=h[0]=" is mis-written; perhaps you meant to write "h_1/e" or something like that.

4. Definitely from less air above you. Lack of molecules might be true as well.

5. Force is FIRST derivitive of U w.r.t. r.
Not sure what "a" is, it might refer to the equilibrium distance between adjacent molecules or atoms.

Hope this helps.

*** An interesting consequence is that, at room temperature, the air pressure drops about 20% for every mile up in altitude. So people in Denver only have 80% as much oxygen to breath as people at sea level. At three miles in altitude, the amount of oxygen is down to about 50% of what it is at sea level. No wonder that people who climb Mt. Everest (6 miles above sea level) need to bring oxygen tanks with them!

Answer 2

Numbers 1 and 4 are the only ones I can help with.
1) I think it's talking about a situation where there is a stable temp in one room and a different stable temp in the room on the other side of the wall. Heat will be flowing from the hotter to the cooler side of the wall. If there's one calorie per second per square inch flowing into the wall there will be the same flow thru all layers and into the cooler room. If some calories got lost in one layer in between, that layer would get hotter than either room. Not gunna happen. It's like electric current in a series circuit, the electron flow rate has to be the same everyplace in the circuit. There's not going to be a concentration of electrons anyplace.

4) It's more the fact that at low altitude, the air has the weight of all the air above sitting on it. Like water in a tank, the pressure at the bottom is due to the water piled up overhead. At higher altitudes, there's not as much overhead.

Answer 3

Good question! But, unfortunately, I practice thermal physics only in bedrooms... :)