Sunday, 17 May 2020

"Lecture 6: Stability [in the atmosphere]"

After much Googling, I have finally found somebody who looks at the bigger picture. From The University of California, Irvine (pdf), slide #5:

What Happens to the Temperature?

• Air molecules in the parcel (or the balloon) have to use their kinetic energy to expand the parcel/balloon
• Therefore, the molecules lose [kinetic] energy and slow down their motions
=> The temperature of the air parcel (or balloon) decreases with elevation...

All the dime store explanations stop right there and ignore the obvious follow-on questions:
- What happens to the heat aka kinetic energy of the legendary 'parcel of air' once it has risen?
- What happens to the temperature of the air that was higher up that is displaced and falls?

These lecture notes cover it very succinctly:

...=> The lost energy is used to increase the potential energy of air molecules.

• Similarly when the air parcel descends, the potential energy of air molecules is converted back to kinetic energy.
=> Air temperature rises.

That kinetic energy isn't "lost", it is just converted to a different type of energy - potential energy. That is the missing figure you need to get the whole atmosphere to balance, despite being the easiest to calculate (mass x height x gravity).

For every parcel that rises, an equal and opposite amount of air must fall elsewhere, which compresses it and causes it to warm up (for two subtly different reasons; the compression itself does not cause the warming, it is the 'falling' that causes both). Which is most of the reason that air is warmer at sea level. The dime store explanation that the sun hits the ground, warms it up and this warms up the air above it etc is only a small part of the bigger picture (it ignores... cloudy days; night time; the fact that two-thirds of the Earth's surface is ocean and stays nearly the same temperature 24/7; and the fact that the Sun shines with the same intensity on the top of mountains).
If this seems far fetched, let me give a real life example:

How can you use water to store electricity?

Clearly you can't, not directly. But you can do the next best thing and use spare night time electricity to pump water up into a reservoir (convert electrical energy to potential energy), then at times of peak demand, you use the water in the reservoir to generate generate hydro-electricity (convert potential energy back into electrical energy).

The air in the atmosphere does exactly the same trade-off, only the trade-off is between heat aka kinetic energy and potential energy.


Derek said...

Right! And then air is a mixture of different gases, the molecules of which each have a mass specific to their type. That presumably means that some of the gases need more energy to reach greater heights. I wonder how that affects things?

Mark Wadsworth said...

D, that's beyond my ken. I think that there are relatively more of the lighter gases higher up.

Dinero said...

My understanding of it is that components of the atmosphere , molecules , bounce off the warm ground transferring heat in vibration and directional movement and Gravity slows down the molecules that bounce off with the most upward proportion of direction the most. Those are the ones that are moving higher, and so the other the molecules that bounce off at a tangent and do not go as high are warmer because they are slowed down less.

Lola said...

see Dinorwic pumped storage. Really cool piece of civil engineering.

Mark Wadsworth said...

Din, I don't think so.

L, "The scheme can supply a maximum power of 1,728-megawatt (2,317,000 hp) and has a storage capacity of around 9.1 GWh (33 TJ)."


Bayard said...

L, there's also this:

Mark Wadsworth said...

B, excellent, let's give it a try.

Physiocrat said...

I am not sure if this is relevant but when a gas is compressed its temperature rises. This is adiabatic compression and used in diesel engines. The Föhn effect is the same phenomenon.

Mark Wadsworth said...

Ph, it is relevant.

Rising (warm) air and falling (cool) air do the equal and opposite things. Temperature of falling air increases for two reasons - it is being compressed slightly and the potential energy is being converted back into heat energy.

Dinero said...

Here is a thermodynamic explanation showing that it is the gravity slowing down the molecule as it moves up.

dT/dz = -g/cp . Change in temp per change in height is equal to the earth gravity multiplied by the change in temp that takes place per unit of energy.

Mark Wadsworth said...

Din, that is more or less what I've been saying all along. Just remember that the heat/kinetic energy is turned into potential energy!

Mark Wadsworth said...

the paper in that link explains this. Only more complicated than the way I explained it. I used the same constants.