If Heat Rises, Why are Mountain Tops Cold? 3

[Barry1492]

Sorry for such a seemingly juvenile question, but I am very weak in Thermo. I understand that heat rises and experience this effect in my house (ie, it is always warmer upstairs in my house). But why then are higher elevations colder than lower ones (ie take the tram to the top of the San Dias Mountains...cold on top).

The concept of heat moving from hot to cold may explain heat rising from an earth surface which radiates heat and moves to a colder higher atmosphere, but why then does heat move from a cold basement to a warm 2nd floor?

If anyone has a clear, simple explanation, I'd be grateful.

-Barry

 

[HVAC68]

All very good explanations. On a similar note, I have another interesting question.

The earth gets heated up by the Sun. We live on the surface of the earth. As you go up, we reach nearer to the sun, eventhough in a miniscule scale compared to the distance between the earth and the sun. By logic, as we go closer to the heat emanating sun, shouldn't it become more hot ???

HVAC68

 

[25362]

Earth's temperature is established by the balance between solar input and infrared radiation into space.

Solar radiation at the outer limit of the atmosphere is about 1370 W/m[sup]2[/sup] (aka solar constant).

Only about 70% of that energy is considered effective solar intensity due to factors such as absorption, scattering and reflection effects by gases and particles, angle of solar rays' incidence, time of the year, etc.

When an object is moving straight up on a clear cloudless day, it indeed gets a bit more radiation from the Sun, as HVAC68 says.

However, there is still the important factor of the equilibrium resulting from reradiation by the object to the surroundings. Since these are cooler at higher atmospheric altitudes (see lapse rate above) radiation from the object to the surroundings becomes stronger.

The formula for the rising object's temperature as a result of radiation equilibrium, disregarding cooling by convection, would be:

T[sub]object[/sub][sup]4[/sup] = (S)(a/b)/[σ] + T[sub]surr[/sub][sup]4[/sup]​

where

S: solar flux, W/m[sup]2[/sup]
a: absorptivity of the object
b: absorptivity of the surroundings
[σ]: Stefan-Boltzmamm constant = 5.669[×]10[sup]-8[/sup] W/(m[sup]2[/sup].K[sup]4[/sup])
T[sub]surr[/sub]: temperature of the surrounding, K
T[sub]object[/sub]: temperature of the object, K

As we can see, as the surrounding temperature drops so does the temperature of the object. If we add convection effects we'd get even lower temperatures. Showing, BTW, the tale of Icarus and Daedalus wasn't (apparently) founded on physical principles.

 

[Barry1492]

Would this be similar to the effect that beech sand has on radiation? In other words, when at the beech I am being radiated directly by the sun but also receive radiation from reflections off the sand and water. If I was to stand on, lets say, grass...less radiation would get reflected toward me. Take that a step further and say I am now dangling in mid air miles above the earth, I now have very little radiation reflected toward me and am only receiving rays directly from the sun.

Is this right?