Warmer on the top of tall buildings

Cecil said that it is cooler on the tops of tall buildings because the air gets cooler the higher up you go. However, inside the building, as hot air rises wouldn’t all the hot air from the lower floors rise to the top of the skyscraper and make the upper floors hotter? This effect works on my two story house, wouldn’t it work even more so on skyscrapers to the point that the upper floors would require much less heating during winter?

Oops, you forgot to link to the column. It makes it easier for everyone in the thread to refer to Cecil’s words. Here you go:Is it warmer at the top of tall buildings?

Penumbra, your hypothesis would certainly be true in a skyscraper that had a broken ventilation system. However, they build those buildings specifically to prevent air from circulating by convection.

What struck me about this column was a rare show of humility from the Perfect Master.

Come on, Cece, you know God has always been lousy at explaining anything. You’re better than Him (by several orders of magnitude).

Perhaps Chronos can explain adiabatic cooling?

Not having knowledge, my old physics texts, nor humility, I can make a weak stab at it. In physics, “adiabatic” means a process that occurs without energy loss. So, adiabatic cooling would mean cooling without energy loss. The question is, what is cooling? The air, or the thing measuring the temperature? I’m going to assume the air.

Heat energy manifests itself as random, molecular motion. The only other ways I can picture the atmosphere storing energy is in organized motion, chemical bonds, or excited electronic states. I can’t believe the last two count in this case. So, the warmest air on the ground surface rises as it expands; as it expands, it cools. This organized motion (outwards in all direction) is adiabatic cooling?

This may be the feeblest Cecil answer I’ve ever seen. Umm, DUH it’s probably colder at the top of the Sears tower … OUTSIDE. But inside the building envelope is a completely different matter, which Cecil, apparently, left to Saltire to even attempt to explain.

More than 20 years and Cece still hasn’t expanded on this thin answer?

Cecil…wasn’t himself then.

Ted Turner has said the top floor of the CNN building is like an oven.

Penumbra is closer to being right, on this one, than Cecil is. Perhaps Cecil is getting burnt out, but he totally misunderstood the question, while Penumbra got it. Granted, it was badly phrased, but the point was still pretty clear.

The OP wasn’t asking about sitting on the roof; she was talking about the heat rising through the building up to the top floor. As Saltire pointed out, this is not an issue in a building with a working HVAC system, nor is there much variation in temperature between the first and hundredth (or whatever) floors when it is working. But, what if it isn’t?

Say the whole system shuts down at 7:00 am on February 29, 2004. The entire building is 70F degrees, give or take. What’s the temperature on the top floor at, say, 4:00 pm versus the temp. on the ground floor? How about at 11:00 pm? Or, 7:00 am the next day?

Probably too many variables to be a practical question, but no where near as dumb as Cecil claimed.

The questioner was going to take suntan lotion to the top of the building instead of going on a tropical vacation. How is it obvious that she was talking about going outside? Anybody can be warmer inside by turing up the thermostat. I think Cecil got it right, FWIW.

The answer about OUTSIDE air temperature is not entirely accurate either. It is true that in the case of the Sears Tower, the air would be cooler. But for a shorter distance, say, 60-90 feet, on a hot day it could indeed be warmer at the higher altitude. I attended an outdoor wedding at a hillside restaurant in Southern California where, outside the restaurant, it was easily 10 degrees warmer than the air on the highway 70 feet below. All other factors being equal, convection and thermals in the air could indeed make the air warmer at elevation, so long as the distance from the ground was within 200 feet or so.

Even for the outside-the-building case I thought Cecil’s response was pretty thin. Anyone who remembers PV = T or even PV = nRT from college physics understands that the atmospheric pressure drop § with altitude results in a corresponding temperature (T) drop. My understanding has always been that this is the primary force affecting temperature change with altitude and the 3 degree/thousand feet rule of thumb.

This is also, BTW, the reason airliners have to run air conditioning at altitude despite being in a sub-zero temperature environment.

Just a thot…

But not only is the volume increasing, which alone could counter the pressure drop, but the energy flow into the atmosphere changes, hence Cecil’s answer. Changes in the energy budget is the reason are regions of the atmosphere which have a much higher temperature than at the Earth’s surface. I suspect you’ll find that one must make assumptions about energy flux, such as hot air rises adiabatically.

Cecil avoided the whole subject of adiabatic cooling, but if anyone is interested, there’s a reasoanbly comprehensible explanation of adiabatic atmospheric processes at http://daphne.palomar.edu/jthorngren/adiabatic_processes.htm

Oldionus of North Hollywood

Wow–adiabatic cooling doesn’t seem that tough to explain (though calculating its effects, etc., would be murder): When a mass of air rises, its pressure decreases, causing it to spread out. This expansion cools the air mass, as the energy of the air molecules is being used to drive the expansion.

toadspittle, you almost summarize the link correctly, but not quite. As the mass of air rises, the pressure of the surrounding air drops, so the “new air” spreads out, and subsequently cools like you said.

If I remember correctly, it is not that hard to calculate. The assumption, or approximation depending on how you look at it, of no heat loss, relates the volume of an ideal gas to the pressure. (That caculation is, as the text boxes used to say, “nontrivial”). But given the relationship, you can use the ideal gas law to compute the temperature drop. I would think the real bear would be computing the volume as a function of time.

The simple idea for ideal gases is PV = T, or it’s more detailed cousin PV = nRT.

P = pressure
V = volume
T = temperature

If the pressure drops and the volume is held constant, the temperature drops. If the volume decreases and the pressure is held constant (tough to do), the temperature drops. If the pressure drops and the volume increases slowly the temperature will still drop.

In the more detailed case n is the number of moles, essentially the molecular count of the gas in the volume V, and R is the universal gas constant. PV = nRT is then the state equation for ideal gases.

Certainly not all gases are ideal, and there is also the assumption that this is for a steady-state system. For the case in question, however, this should be very accurate.

The relationship doesn’t require heat to be added or extracted, since T describes the heat content. Adding or extracting heat changes T and the effects on P and V are then described by the equation as well.

This isn’t that tough to get one’s head around, in my opinion, especially in the most fundamental form of PV = T. Certainly Cecil has gone into far more technical depth on more esoteric topics, so I was disappointed that he missed this simple explanation.

OK. The original answer may be correct based on abstract, theoretical principles. As one rises in altitude, temprature drops. However, I am sure that one could find easily find localized points where this does not hold true.

A very easy example may be found on the Island of Manhattan. During the afternoon the streets are in shadow while the tops of the buildings receive sunlight. A person standing on the roof of 45 Wall Street may be warmer than somebody standing on street level.

Another example is Buffalo, NY. Cold winds coming off the the lake may cool the first few floors of a building, but higher up, the chilling effects of the wind may be diminished.

I do not mean to diminish the original column, but there may be “exceptions that prove the rule.”

A major point of adiabatic cooling is that the volume, for the same number of moles, is not constant. When hot air rises, it expands. (The number of moles within some given volume is changing.) The ideal gas law, in and of itself, is insufficient. Knowing nothing more, it is impossible to state what happens to the temperature, because the volume could increase faster than the pressure decreases. The presumption of adiabatic cooling allows one to relate the pressure to the volume (or the change in n for a given volume) and thus use the ideal gas law to show that the temperature drops. (If I remember correctly, in adiabatic cooling the PV goes like Volume^(1-gamma), where gamma depends on the molecular structure of the substance. In this case, I believe it is 4/3, or maybe 5/3, so as the air expands, the temperature drops slowly.

I also think James Bond has a point. Buildings are known to absorb a significant amount of solar energy, hence the difficulty in cooling them. Since the upper reaches of the tallest buildings are exposed light for longer periods, it is easy to believe there is some localized heating.

I’m not disputing that adiabatic cooling also takes place as warm air rises, or that urban canyons in shadows won’t get warmed by the sun as much as higher sunlit roofs, but the most general explanation of why it gets cooler as one goes up in altitude is PV = T, and this was completely missed in Cecil’s answer.

Sure, talking about adiabatic cooling is fine for the case where there is warm air rising. That is an important, but not necessarily most general, case. And several here have provided nice synopses of adiabatic cooling, too, so why the uncharacteristically incomplete response from Cecil, even in a 20-year repeat?

I think this is getting beaten to death pretty thoroughly.

The tops of buildings, especially tall ones,
with lots of mechanical equipment on top, may dissipate enough heat raise the immediate temperature on the rooftop relative to ambient air temperatures. You might be able to suntan comfortably on an otherwise chiily spring day.

Climbersam hit on my thought. With the various equipment on building tops - heat exchangers, being one, I can easily see skyscraper rooftops being warmer than the weatherman suggests. Also, many commercial rooftops are covered with black, heat absorbing material.

First, let me start by stating that I agree with others. There are undoubtedly more effects here than the simple “it gets cold when you climb a mountain”. (Where do they vent the output of the cooling system?)
But, with respect to:

ejacobsen, I’m afraid you are wrong. The temperature of the atmosphere does not drop uniformly as you climb to the space station. There are layers of the atmosphere that have a very high temperature.

In fact, an object sitting at earth’s orbit, and rotating, will have a mean temperature comparable to the earth’s - even though the pressure is zero. PV = nRT explains what happens to closed containers as you play with the four variables.