Regarding the previous post, if the atmosphere of the planet in was initially at a uniform temperature for all heights above the surface, it would seem the temperature would tend to remain uniform.

No, it wouldn't, because it would not be in hydrostatic equilibrium.

 

I no longer have my meteorology book from college, so can you provide any links that explain the conditions for hydrostatic equilibrium of the atmosphere and the relationship between temperature and pressure?

 

Have you heard of Google and/or Wikipedia?

https://en.wikipedia.org/wiki/Lapse_rate#Dry_adiabatic_lapse_rate

 

I read the article:

https://en.wikipedia.org/wiki/Lapse_rate#Dry_adiabatic_lapse_rate

The conditions it describes are adiabatic where no heat enters or leaves the parcel of air while it rises or falls. Also, the atmosphere is presumed to be in hydrostatic equilibrium (a static condition with no vertical or horizontal convection) so movement of the parcel will independent of any other forces.

However, air movement is not adiabatic and the parcel will release heat through various channels such as conduction and radiation. Eventually, it's temperature will approach equality with its surroundings. If the atmosphere is static, the temperature will be the same at any height.

 

If the atmosphere is static, the temperature will be the same at any height.

This is not true. You need to account for the effect of gravity.

If you throw a ball up into the air, as the height increases the speed decreases, some of it's KE turns into gravitational PE. The same is true for air molecules, if they rise a height 'h' they slow down from the pull of gravity, the drop in KE is mgh, this fact alone results in a lapse rate of:
change in KE = change in 5/2kT = -mgh

substitute in for m ≈ 29AMU gives a lapse rate of 13.7C/km (the actual rate is 9.8C/km).

This is not the whole story as you have to account for the work done on a parcel of air as its volume changes, but I think this helps understand what is happening. (Unless Cunningham's law proves me wrong!).

 

I read the article:

https://en.wikipedia.org/wiki/Lapse_rate#Dry_adiabatic_lapse_rate

The conditions it describes are adiabatic where no heat enters or leaves the parcel of air while it rises or falls. Also, the atmosphere is presumed to be in hydrostatic equilibrium (a static condition with no vertical or horizontal convection) so movement of the parcel will independent of any other forces.

However, air movement is not adiabatic and the parcel will release heat through various channels such as conduction and radiation. Eventually, it's temperature will approach equality with its surroundings. If the atmosphere is static, the temperature will be the same at any height.

Simply not true. There's this little thing called gravity that you are conveniently forgetting. Analyzing a parcel of air as it is moved vertically in order to determine the conditions needed for static equilibrium is just a tool. Similar approaches are used to analyze many systems, including electronic ones.

 

OK - If I have a vertical scuba tank that's sealed and fully pressurized, is the temperature at the bottom going to be higher than at the top?

 

I believe it would, if it had the same gravitational gradient as the atmosphere.

 

If the mass of air in the tank is fully at rest, how would the influence of gravity cause this temperature variation?

 

Gravity will cause a density gradient.

The bottom of the tank will absorb more IR than the top of the tank. Not only because the bottom is closer to the source, but there is more mass at the bottom to absorb it.

This causes a temperature gradient.

This causes heat flow.

 

The definition of adiabatic lapse rate assumes that no heat enters or leaves the atmosphere or the tank in my example.

So how does that cause the temperature at the bottom to be higher than the top?

 

Pardon me. I thought you were comparing a vertical pressurized tank, with a column of atmosphere.

 

If the height of the vertical tank is 30,000 feet and the diameter is one foot, how would the temperature vary with height?

 

I believe it's 2-4 degrees, depending on what scale, for every thousand feet.

 

OK - If I have a vertical scuba tank that's sealed and fully pressurized, is the temperature at the bottom going to be higher than at the top?

Assuming we could treat it as a column of free air, yes, but only minutely so --perhaps a few milliKelvins. Having said that, the two aren't really comparable because the tank walls establish thermal conditions at the boundaries and so you can't treat it as a column of free air. But let's ignore that.

Would you agree that the pressure at the bottom of the tank is greater than the pressure at the top of the tank?

Would you agree that the density at the bottom of the tank is greater than the density at the top of the tank?

Would you agree that the rate at which the pressure and density changes as you rise in the tank aren't arbitrary, but have to follow a specific profile in order to establish equilibrium?

Would you agree that the temperature at any particular height in the tank affects the pressure and the density at that height in the tank?

Would you then agree that the temperature as a function of height isn't arbitrary, but rather has to follow whatever profile the ideal gas law dictates in order to establish the necessary pressure and density profile?

 

If the mass of air in the tank is fully at rest, how would the influence of gravity cause this temperature variation?

Because the ideal gas law has to be satisfied as the necessary pressure and density gradients are established.

 

If the height of the vertical tank is 30,000 feet and the diameter is one foot, how would the temperature vary with height?

With those dimensions, the temperature would be driven by the tank walls and not by free-air processes.

 

They beat it into our heads in physics that warm air does not 'rise',
Warm air is forced up by the colder , denser air below it.

/Clay

 

They beat it into our heads in physics that warm air does not 'rise',
Warm air is forced up by the colder , denser air below it.

That's mostly semantics; six of one, half dozen of the other.

But the truth in that beating is that gravity acts on mass, pulling masses together. There is no force that causes rising, per se. The floating of a boat is the result of gravity pulling the water down more forcefully than the boat, displacing the boat to the surface. Turn off gravity and the boat is just as likely to sink as to float away.

I'm with WBahn on the cause for cold temperature at high elevation, which is a well known phenomenon to anyone that flies or climbs mountains. An imaginary, stable column of air, with no energy coming in or out, without bulk mass moving within the column, will show a temperature gradient. It's a thermodynamic certainty.