March 14th, 2017, 08:25 PM  #1 
Newbie Joined: Feb 2017 From: Lebanon Posts: 15 Thanks: 0  Hot air theory
I was recently reading an article named "The air cooler in the mountains". After reading about the whle article i have one question now. Can any one give me such specification so that I can clear the concept. Question is: " If hot air rises, why is it generally colder at higher elevations? " 
March 14th, 2017, 08:54 PM  #2 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,166 Thanks: 173 
There are many reasons. Hot air doesn't stay hot , it cools. The atmosphere is thinner at higher elevations. There are very few objects at higher elevations , less chance for radiating heat. The Earth gives off heat , as you distance yourself from the surface the heat genrated by the Earth cools off. People , organisms and artificial man made objects give off heat , there are less of those at higher elevations. i'm sure there are quite a few other reasons 
March 15th, 2017, 01:12 AM  #3 
Senior Member Joined: Jun 2015 From: England Posts: 513 Thanks: 133 
Don't forget when we are talking about air temperature we mean the general temperature of the still (non moving) air at any particular elevation. Locally moving parcels of air can be warmer or colder than this. We take special precautions when measuring air temperature scientifically to still the air and prevent other unwanted influences as well. That is why if you just place thermometers around you will find some apparantly results. The air gets it heat mainly from contact with the ground so the further up you are the colder the air, until you get way up into the upper atmosphere. There is a quantity known as the adiabatic lapse rate, which measures this. https://www.google.co.uk/search?hl=e...48.N3oNZ_Vt8P4 
March 15th, 2017, 03:31 AM  #4  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 1,895 Thanks: 614 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
2. Because of the balance of forces, density in a medium is rarely constant and often decreases with increasing height (i.e. can be considered a 1D system based on height). 3. Density perturbations often arise in diffuse media, which are small 'parcels' of mass having slightly different properties to the rest of the environment. This gives rise to a physical treatment comparing the state of the "environment" with the state of "perturbations" at a particular height. 4. If the perturbation is a slight increase in density, the parcel is heavier than the surrounding matter, so it sinks. 5. If the perturbation is a slight decrease in density, the parcel is lighter than the surrounding matter, so it rises. 6. The parcel has an equation of state (e.g. ideal gas), so as it rises or sinks, it changes its pressure, volume, temperature and density. 7. If: a) the change in state of the parcel causes the density to be closer (less different) to that of the surroundings, then the atmosphere is one that stabilizes against a perturbation and convection does not occur. b) the change in state of the parcel causes the density to be more different than that of the surroundings, then the atmosphere is one that is unstable against perturbations and convection occurs. 8. Therefore, density gradients of perturbations compared with the environment give rise to whether convection occurs. By plotting the density gradients of an "environment" versus "perturbations" as a function of height, the convection zones can be obtained. Convection zones cause convective mixing and tend to homogenise the state of the environment. 9. For the specific case of the Earth, its atmosphere usually stabilises perturbations and therefore isn't one massive convection zone. The atmosphere doesn't mix wholesale, so we have the force balance result (points 1 and 2). Note that the entire above scenario can work with any variable in the equation of state, including temperature, pressure or composition. Because of this, there are often different forms of convection occurring at different parts of the Earth (e.g. semiconvection or thermohaline mixing). This also means that oceans can convect through temperature differences, even though liquids are relatively incompressible compared with gases or plasmas. Also, a lot of the interesting convective behaviour requires using 3D geometries rather than 1D ones, so the problem of convection zones of the Earth's atmosphere or oceans becomes much more difficult than the above, simplified scenario. Last edited by Benit13; March 15th, 2017 at 03:43 AM.  
March 15th, 2017, 11:17 PM  #5 
Newbie Joined: Feb 2017 From: Lebanon Posts: 15 Thanks: 0  Hot air theory 
March 16th, 2017, 02:02 AM  #6 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,166 Thanks: 173 
Everything loses energy as time passes. No real environment is ideal. When gasses expand they cool. As you go to higher elevations the radius of the spherical atmosphere increases so there is more spherical volume available for the gas to expand into and cool. The hot air interacts with cooler air as it rises until relative equilibrium temperature is reached. Everything is a process of negotiation in a rather chaotic state subject to the forces of nature (physics) Last edited by agentredlum; March 16th, 2017 at 02:11 AM. 
March 16th, 2017, 02:35 AM  #7  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 1,895 Thanks: 614 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
In the vast majority of circumstances, yes. However, there are some exceptions. I'm not sure about terrestrial atmospheres, but stellar interiors can sometimes have regions with density gradients increasing with height instead of decreasing because of changes in composition of the plasma. This gives rise to really unusual mixing phenomena, like doublediffusive mixing.  

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