
#19
Apr2312, 01:26 PM

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#20
Apr2412, 07:44 AM

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If a parcel of air expands a little, for whatever reason, it expands the total volume of the atmosphere that much. This means the average height of the molecules in it has increased. So work is done adding to the potential energy. This is quite different from a closed box, and the reason it does not warm another parcel of air.
I think a lot of the confusion over this topic arises because people think of this process as causing the air to be colder higher up. If you could stop the convection, by inserting baffles all the way up, the temperature gradient would be far steeper. The tendency of air to cool when lofted to a lower pressure altitude inhibits such movements, and they only occur when the temperature gradient is steep enough to overcome it. So the expansion doesn't cause it to be colder higher up, it just limits convection's ability to prevent its being so. At the tropopause, the gradient is no longer steep enough and convection largely ceases. 



#21
Apr2512, 07:17 PM

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A cube shaped block of air whose volume is one cubic kilometers expands with force 100 Giga Newtons. That is the force of air pressure on one side of the cube.
If the volume increases 20 %, the energy of expansion will be 200 meters * 100 Giga Newtons = 20 Tera Joules. That's 20 Kilo Joules per one cubic meter, which has mass of about 1 kg, which cools about 20 degrees when 20 Kilo Joules of energy leaves it. Now we want to know where the energy goes. Well it goes everywhere at speed of sound. Because the expansion causes a slight air pressure increase everywhere. 



#22
Apr2512, 11:36 PM

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Average air pressure at Earth's surface must be total weight of atmosphere divided by area. Increasing the volume of some of the air does not increase its total mass. If anything, it will decrease total weight slightly because the average height of the air molecules increases. The energy goes into the atmosphere's gravitational potential energy. 



#23
Apr2612, 03:37 AM

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But the energy to lift the atmosphere travels around the atmosphere as pressure wave and at speed of sound. 



#24
Apr2912, 03:21 AM

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#25
Apr2912, 04:26 AM

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[itex]\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}[/itex] and V_{2} = 2V_{1} then [itex]\frac{V_{1}}{T_{1}}=\frac{2V_{1}}{T_{2}}[/itex] ∴ T_{2} = 2T_{1} from which we end up with Charles's Gas Law, which states that, at constant pressure, the volume of an ideal gas is directly proportional to its temperature. http://en.wikipedia.org/wiki/Charles%27s_law 



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Apr2912, 06:38 PM

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Apr2912, 06:43 PM

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Apr3012, 05:42 AM

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#29
Apr3012, 05:46 PM

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This risingexpandinggetting dense cycle has diminishing returns, so settles out when the air is at the same temperature as surrounding air. (This is for dry air  moist air is more complicated.) At the same time, some air must descend to occupy the space vacated. That air gets compressed adiabatically, warming. Looking at the total picture, the air as a whole is a little warmer than before (we added heat to kick this off), so is a little less dense, so the atmosphere extends a little further into space and has acquired a little extra potential energy. Thus the heat energy lost by the ascending air has not quite all gone into heating the descending air. 



#30
May112, 03:37 AM

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#31
May112, 05:52 AM

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What you are describing is what happens at the surface: it is heated and expands at constant pressure. That's what causes it to rise. 



#32
May112, 05:53 AM

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http://apollo.lsc.vsc.edu/classes/me...diab_cool.html 



#33
May112, 05:55 AM

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I was *only* pointing out that Charle's Gas Law, which Dave mentioned, requires constant pressure. It was offtopic, I guess, technically, because I wasn't trying to add anything to the discussion of why it gets colder with increasing altitude. 



#34
May112, 06:09 AM

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Yes, you're right, sorry. Dave used the right term for what was happening but applied the wrong equation. That's what I get for only reading half a post.




#35
May112, 07:22 AM

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I quote the original question and the simplest answer must explain the steady state, static condition, not involving convection / mixing / adiabatic cooling / heating by the ground etc.. Consider a simple column of a gas air, in equilibrium in an insulated cylinder. In an equilibrium situation the air at the bottom of the column will not rise if it is MORE DENSE than the air above it. This can occur even when it is 'warmer', as long as the pressure is greater. So a temperature / pressure profile can occur which will not allow convection but where the temperature at the bottom is higher than the temperature at the top. The atmospheric pressure is approximately halved for every 5km increase in height (for constant temperature). Applying P_{1}V_{1}/T_{1} = P_{2}V_{2}/T_{2} to this simple model of a column seems to indicate that a mass of air at sea level at a temperature 300K will occupy a smaller volume than the same mass of air at 5km height (half the pressure), if the temperature at 5km is greater than 150K. (Someone else please check this) This result is extreme and not realistic but it makes the point, I think. There are many other factors at work but it does put to bed the notion that the Hot Air must rise up through the Cold Air. 



#36
May112, 08:08 AM

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This isolated column is not a good model of the Earth's atmosphere. The Earth's atmosphere is not an isolated system and it is far from thermal equilibrium. The atmosphere is primarily heated from below and radiates into space from above. The atmosphere is typically closer to that local max (adiabatic lapse rate) than it is to the global max (constant temperature), so the atmosphere is typically driven toward that local max in which temperature decreases with altitude. But not always. Sometimes thermal inversion layers set up in the atmosphere. Rising air stops at the inversion layer  until it finally punches through. That's when all kinds of havoc such as tornados can result. 


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