Temperature and pressure

[redblue]

Can someone offers an explanation of how temperature affects pressure in the free atmosphere? A book I am reading says a cold front brings "A sharp fall in temperature, a rise in presure." But searching online I found some places describing an increase in temperature brings a rise in pressure.

There are two theories that appears to contradict:
1) A hot area heats up the air above it and lifts this, causing the surrounding air to flow into this area of "low" pressure.
2) A hot area lifts the air above it, expanding this column of air. So if you are at 1,000 ft measuring the pressure, the station pressure should reflect an increase in pressure with more air molecules rising above you over time.

Is there a book that can provide a very good explanation of temperature and pressure? Better if it utilizes math. And also explanation of the conversion, especially the reduction part, of the Qs (ie QNE, QNH, QFE, etc)

Thanks.

[enicalyth]

For a dry ideal gas Volume/Temperature is a constant provided that Pressure stays the same (Charles' Law).

Pressure * Volume is a constant provided that Temperature stays the same (Boyle's Law).

Combine the two and for a dry ideal gas PV/T is a constant. So if you have two states denoted y suscrits 1 & 2 you can write P1V1/T1 = P2V2/T2. Teerature has to easured (y keyoard can't sell) in asolute units When it coes to wet air it gets a little awkward I can't write now the keys are screwed!

[XPMorten]

I think your book means that if its a front, it MOVES, and a cold front is often
followed by a high which would explain the pressure increase.. .

Cheers,

Morten

[BOAC]

The simplest (KISS) way I have always taught it is:

Draw a sloping front on a piece of paper. mark 'C' under the slope (for 'Cold') and 'H' above.

Cold air is more dense than hot - OK?

Now draw two vertical columns, one in the hot air and one in the cold air, passing into the hot (through the front).

You will replace the bottom of the hot column with colder, denser air as the front moves across. More mass of air in the column = more pressure.

Plenty of info on QNH/QFE etc via Google if you look or perhaps a met man with spare time will help.

[bookworm]

The short answer is that the relationship is not a simple one but depends on many other factors.

The example that you give of a cold front has more to do with the nature of the shape of isobars around a Low with fronts trailing from it than a direct relationship between temperature and pressure. The low will tend to move parallel to the warm sector isobars, so as the cold front passes, the pressure will rise.

If you heat a column of air, causing it to rise, it will tend to expand upwards, thus creating a core of higher pressure at the upper levels. This causes it to diverge a little at the upper levels as the, in effect, drifts out from the high pressure core. In turn, that means less air in the column, and so less pressure at low level. Thus, all else being equal, a column of hot air will tend to be associated with low pressure close to the surface, and high pressure in the upper levels.

Put another way, the rate of decrease of pressure with height is inversely proportional to the temperature.

Does that help to reconcile your apparently contradictory "theories"?

[barit1]

The thing to remember is that Boyle's and Charles' Laws apply only to static control volumes in which the parameters (T, P, energy...) are constant throughout. The met problem (frontal passage etc.) is a problem of dynamic conditions with uneven energy levels around the atmospheric map. Thus a high pressure region may indeed be a cool region as well - maybe a met guy can give us some insight re what drives this phenomenon.

[redblue]

If you heat a column of air, causing it to rise, it will tend to expand upwards, thus creating a core of higher pressure at the upper levels.
Why does it create higher pressure at the higher altitude though. Afterall, the atmosphere is not enclosed so it isn't like heating the gas inside a closed box.

Now, I do remember having read something about this phenomenon about upper and lower levels having different pressures due to heating.

And yes, I did search for the Qs online and in the books. But whenever they attempt to explain how to extrapolate for surface pressure after having measured the station pressure at a higher altitude, they describe it instead of providing math examples. For example, it station pressure at 1,000 ft is 28.92" at 10 degrees, how does one get the sea level pressure?

[BOAC]

Once again, using the KISS princilple, and reaching back (with apologies) to the dark recesses of my brain (some 38 years ago), I seem to remember the CFS 'simple' answer was to again draw two vertical columns, one high and hot and one low and cold.

Assume the same surface pressure and 'nothing' above the top of each column.

At any point, if you take a horizontal plane, the pressure in the hot will be greater than in the cold, since the air below is less dense, but the TOTAL weight of air in each column is the same.

As far as QNH calculations are concerned, we need a met man, but I ASSUME the pressure is adjusted at the standard lapse rate for pressure/1000' at the given OAT - and from a table? EG If the OAT was 12deg C at 1000', that would be pretty well ICAO, and I guess the 1mb/30 ft would apply? Given, therefore, a baro reading of 970mb there, I guess the 'QNH' would be 1003mb (ish)? (KISS again!). Sorry I cannot do that in inches, as they say:D

[redblue]

Is there a book that can explain all these in very detailed terms? Did you take a class on this before when you said reaching back trying to remember? If so, which textbook did you use?

[BOAC]

Is there a book that can explain all these in very detailed terms? Did you take a class on this before when you said reaching back trying to remember? If so, which textbook did you use?

I cannot recall which 'book' we used - it may have been a RAF publication, some of which were excellent.

Without prying too deeply, though, 'redblue', looking at your profile, can you not just 'accept' these apparently contradictory/confusing items and live with them for PPL work? If you are looking at becoming a met man, I sugggest you contact your local aviation met office and ask them for a pointer at books. If you are going 'commercial', the training course will cover all you NEED to know (for the exam:D ). The ONLY reason I had to know them was in case 'Bloggs' asked me!!:D I don't think I have ever used the info for real in 40yrs plus flying!

[bookworm]

Why does it create higher pressure at the higher altitude though. Afterall, the atmosphere is not enclosed so it isn't like heating the gas inside a closed box.

The mental model that I use, rather like BOAC's, is that of a column of air with pressure levels marked as stripes. If the air is warmer than the surrounding air, the column will stretch like a concertina, and the vertical separation between the stripes will be greater than in the surrounding air. Thus if the pressure levels are aligned at the surface, the warmer air will have higher pressure than its surroundings at the top. In reality, things will equilibrate a little, and there will tend to be lower pressure at the surface, and higher pressure at the top.

If you don't like the model of the atmosphere expanding in vertical columns, that's fair enough, but what is determined by the laws of physics is the separation between pressure levels as a function of the temperature of the air.

For books, I'd recommend Bradbury (http://www.amazon.co.uk/exec/obidos/ASIN/0713668318) and possibly Stull (http://www.amazon.co.uk/exec/obidos/ASIN/0534372147).