Indeed, in response to Pekka, isentropic processes are difficult to find, and only exist when the state is isentropic. In an isentropic state, which for the atmosphere would be a dry adiabatic lapse rate, no amount of mixing will change that state. In any other non-isentropic state, mixing will increase the entropy, and this includes the isothermal state as an example. Vaughan Pratt wonders why I think potential temperature is a conserved property under other processes. In a gas, potential temperature is the conserved thermodynamic quantity in the absence of any diabatic effects. It is derived from dQ=T*dS=cp*dT-V*dP. Setting dQ=0 and using the ideal gas law you can find that a conserved quantity is cp*dT/T-R*dP/P and define a quantity theta=T/(P/P0)^R/cp which is potential temperature and where P0 is a reference pressure where theta is chosen equal to T (sea-level pressure). The only condition to conserve this is that dQ=0 (adiabatic processes). Conduction and diffusion are adiabatic processes assuming the gas is isolated and has no heat flux through any boundaries. We also see that dS=cp*d(theta)/theta, so that log(theta) is proportional to entropy.

“I have to agree with Jim D. that potential temperature is conserved in the case of heat transport by convection. After all it’s the motivating property of potential temperature.”

Yes, I am also agreeing with him on that score.

“What I don’t understand is why he believes that potential temperature is also conserved by other transports such as conduction or diffusion. So far his only proof seems to be that if it is preserved by convection then it must also be preserved by other transports. That’s not a terribly convincing argument.”

Exactly. So far as I can see, his main mistake is to assimilate two completely different sorts of ‘mixing’ processes, because both of them can be enhances at once through stirring a pot with a wooden spoon. The processes still are radically different. The first requires (or generates) work and is isentropic. This is the displacement of macroscopic air parcels that are allowed to contract and expand while dU = dW = P(t)dV at all times. The second process is the equilibration of thermal gradients from molecular diffusion, and is spontaneous (doesn’t require work) and irreversible. The first process is reversible. The simultaneous operation of the two processes drives the gradient towards the adiabatic lapse rate, but it requires an energy input (or an initial profile that is steeper than the adiabat and hence unstable). When the external energy source is shut of, the first process dies down and only the second remains. The heat flow bring the column back towards isothermal (regardless of the gravitational acceleration spatial variations, so long as the external force field is stationary and conservative along closed paths).

P-N, “To be clear, in this thread I’ve always used “isothermal profile” to refer to a property of the combined vertical temperature and pressure profiles such that the (slow) vertical displacement of any air parcels would be a reversible *process* that conserves potential temperature as it adjusts to the pressure of the surrounding.”

I was a bit confused on whether you were considering totally isothermal or an isothermal profile. There is not a huge difference between an isothermal profile and an adiabatic profile. The largest changes are when actual specific heat capacity ratios are considered which would be when there are mixed mass particles that could be segregated by gravity, JimD’s case.

That is when I mentioned for a perfectly isothermal atmosphere you would need real containment, gravity by itself would likely not do the job especially if there is rotational velocity to be considered.

With an isothermal versus adiabatic profile it is easy to see why some would think the G-T effect might provide usable energy, but then there is an issue with energy density versus a temperature gradient. In other words, potential energy cannot be converted to work without movement and a few bouncing molecules would not produce much energy. You would need the same number of molecule at different kinetic energy to produce a flow and at the top of the column there would be a small percentage of molecules with lower/higher than average KE.

I could see a very tall useless, perpetual motion toy for a huge skyscraper atrium being built in some place like Dubai or some other place with lots of money to throw away on “art”. I think a serious glass enclosure would be recommended though.

“Do you really mean “isothermal profile” in your latest comment to me. I think, you must have had “isentropic profile” in mind.”

Yes, absolutely. Thanks Pekka. (I also sometimes say troposphere when I mean stratosphere. Never trust my words.)

If nuclear is the only option we might as well move back into caves.

Solar is the answer. Just 10% of the Texas panhandle covered with bio-reactors can produce enough transportation fuel for the entire United States at a lower cost than today. The problems are tractable with the main one being delivering enough concentrated CO2. The technology however is scalable so small bio-fuel factories can be paired with CO2 production points. Ultimatel, as synthetic biology is mastered, the bio-reactors build themselves like a tree builds itself only far more complex with plumbing spanning whatever distances are needed, storage tanks, the whole nine yards. Concentrated CO2 is only needed today because the bio-reactors are manufactured from plastics and similar materials to they’re too expensive to operate at low efficiency with atmospheric CO2. When synthetic biology gets to the point where the bio-reactors themselves are self-replicating then they’re essentially free so they can make up in quantity what they lack in efficiency.

There are no breakthrough technologies required for the above. Nature already has all the systems designed and tested it’s all just reverse engineering for us. It’s like cut & paste with DNA. Laboratory tools that reduce the labor required in the reverse engineering are growing faster and less expensive at a rate commensurate with Moore’s Law for semi-conductors. It’s the path that requires the least time because the technological progress is exponential and deployment becomes exponential as well with self-replicating components.

This is essentially nano-technology on a trajectory that was predicted back in the mid-1980’s with a predicted time to maturation of about 50 years. Thirty years later it’s right on track. Stuff we’re doing today with micro-biology labs was almost inconceivable 30 years ago. We now have centimeter square chips that have the equivalent of thousands of test tubes on them. What took months and many technicians and a large biology lab now takes hours with almost no human intervention. Almost inconceivable. Some visionaries saw it. I was fortunate enough to have followed those visionaries from the word go. Computing power and a global hyper-text network was one of the prerequisites. Synthetic biology requires data-storage, processing, and collaboration on a large scale. The machinery of life, even simple bacteria with minimal genomes, are more complex than any machines or machine complexes ever designed by human engineers. The reverse engineering effort required is huge but manageable. The computing part and a lot of the biological part is done. The first living, reproducing bacteria with a 100% synthetic genome was brought to life a few years ago by Craig Venter … http://en.wikipedia.org/wiki/Craig_Venter it’s only a matter of time before biofuels become cheaper than equivalent fuels made from crude oil ever were.

Jim,

What is heat conduction?

It’s transfer of heat from one subsystem to another. It’s transfer of heat from the warmer subsystem to the cooler one. That’s not adiabatic for either of the subsystems. That increases entropy of the combination of these subsystems. You cannot discuss anything of interest in thermodynamics without dividing the overall system to subsystems. Everything that you have discussed involves subsystems.

You can find statements that thermodynamic equilibrium is isothermal in virtually every textbook that discusses thermodynamics. As an example you can find the following sentences in Pierrehumbert’s book in the chapter 2.3.3 Entropy, reversibility, and potential temperature; the Second Law:

The Second Law is perhaps more intuitive when restated in the following way: In an energetically closed system, heat flows from a hotter part of the system to a colder part of the system causing the system to evolve toward a state of uniform temperature.

Further in the chapter he discusses the potential temperature, but nowhere is any hint that the above sentence should be modified or that it were true for the potential temperature. As virtually every physicist, he knows well that the sentence is true for the temperature, not for the potential temperature.

For the discussion of isothermal self gravitating systems at equilibrium such as gas clusters (in some conditions), see the following reference:

P. H. Chavanis, ‘Gravitational instability of isothermal and polytropic spheres’

http://judithcurry.com/2014/12/01/gravito-thermal-discussion-thread/#comment-653279

Are those percanteges for capacity installed or generated Energy?

Planning Engineer. Is this just government hype, or could there be a serious problem? I know there have been some disruptions to the power system from solar storms before, but this article has the ring of “catastrophe” to it. We’ve heard so many exaggerated claims of danger from this or that natural phenomenon before, I’m always wary. Boy – wolf …

From the article:
DHS: 100 Million Americans Could Lose Power in Major Sun Storm
Document says FEMA unsure of damage to grid from magnetic storm
SHARE
TWEET
EMAIL
Sun emits a mid-level flare – 04 Dec 2014Sun emits a mid-level flare Dec. 4, 2014 / AP

BY: Bill Gertz
December 12, 2014 5:00 am

Millions of Americans face catastrophic loss of electrical power during a future magnetic space storm that will disrupt the electric grid and cause cascading infrastructure failures, according to a Department of Homeland Security (DHS) document.

DHS’ Federal Emergency Management Agency (FEMA) stated in an internal 2012 fact sheet outlining its response plan for severe “space weather” that the actual impact and damage from a future solar storm is not known.

“An analysis of the space weather impacts indicates that the greatest challenge will be to provide life-saving and life-sustaining resources for large numbers of people that experience long-term power outage from damage to the U.S. electrical grid,” the FEMA document, dated March 1, 2012, states.

The FEMA fact sheet noted the findings of a 2010 study by the National Oceanic and Atmospheric Administration, the agency that monitors sun storms, warning that an extreme solar storm could leave “130 million people without power for years,” and destroy or damage more than 300 hard-to-replace electrical grid transformers.

– See more at: http://freebeacon.com/national-security/dhs-100-million-americans-could-lose-power-in-major-sun-storm/#sthash.4hR7iAr5.dpuf

…

http://freebeacon.com/national-security/dhs-100-million-americans-could-lose-power-in-major-sun-storm/

If Texas were a nation it would be 40th largest by geography right behind Chile and have the 14th largest economy. It most certainly can be considered in isolation. Among the nation’s contiguous 48 states, Texas is the only one that has a stand-alone electric grid entirely within the state. It is quite isolated from the eastern and western national grids. Electrical energy import/export is practically nil.

http://www.eia.gov/state/analysis.cfm?sid=TX

Electricity

Texas produces more electricity than any other state, generating almost twice as much as the next largest generating state. More than two-thirds of the electricity generated is from independent power producers. Almost half of the electricity generated in Texas comes from natural gas-fired power plants, while coal-fired power plants account for about one-third of the net electricity generation. Six of the state’s 10 largest power plants are coal-fired. Two nuclear plants, Comanche Peak and South Texas Project, supply nearly one-tenth of the state’s electric power generation. The rest of the electricity generated in Texas is powered by renewable resources, primarily wind.

Texas is the largest electricity-consuming state. Unlike other regions where large net interstate electricity deliveries are available, the Texas power grid is largely isolated from the interconnected power grids serving the eastern and western United States. This isolation means the state is, for the most part, dependent on its own resources to meet its electricity needs, and it is not subject to federal rules. Among the contiguous 48 states, Texas is the only one that has a stand-alone electric grid entirely within the state.

The largest share of retail electricity sales in Texas is to the residential sector. Almost six-tenths of the households in the state use electricity as their primary heating fuel. The residential use of electricity is higher in Texas than in other states, in part because of population size, but also because of high demand for air conditioning during the hot summer months and the widespread use of electricity for home heating during the generally mild winter months.

There are a couple of ways to address the kinds of concerns Pekka puts forwards.
First, you end up with a contradiction if you say that an isentropic state will diffuse heat in such a way that it ends up isothermal. The isothermal state with the same total potential temperature, but now a gradient of potential temperature, has a lower entropy, which makes this an impossible process to occur spontaneously.
Second, mechanistically what is molecular diffusion? It is the transfer of energy by collisions. Starting isothermal, particles from above will have gained kinetic energy from potential energy and those from below will have lost it by the time they collide at some reference level. This systematic correlation between motion and KE means that there is a downward flux of energy through the reference level. Only when the upper layer has cooled sufficiently is this PE gain canceled by the KE gradient. Heat is transferred down a potential temperature gradient, not just by eddies, but also by molecules. There is no reason for these two processes to respond differently to gravity.

Jim,

You continue to claim that constant potential temperature would have a higher entropy than isothermal that has the same total energy. Your statement is wrong. The truth is the opposite as virtually every textbook tells.

“such as [star] clusters…” (Though the discussion generalizes to other self gravitating systems)

Pekka, no, a potential temperature gradient with the same total potential temperature has a lower entropy than that same total mixed into a uniform value. You can prove it by using two equal-mass layers as an approximation of a gradient. It follows from entropy going as log(theta).
0.5*[log(theta1)+log(theta2)] is less than log[0.5*(theta1+theta2)]. It is because the geometric mean of any two numbers is always less than their arithmetic mean.

Origine 2013 de l’électricité vendue par EDF
I use EDF’s electricity supply in my property; they are currently obliged to inform their customers where the consumed electricity came from.

Jim D wrote: “[…] Second, mechanistically what is molecular diffusion? It is the transfer of energy by collisions. Starting isothermal, particles from above will have gained kinetic energy from potential energy and those from below will have lost it by the time they collide at some reference level.”

In the stationary isothermal equilibrium state, (which also exhibits a barometric density profile; though the following consideration is valid regardless of this,) at any level z = h, as many molecules cross it going up as do going down. Each molecular trajectory is a parabola that crosses this level with the same identical speed while going up as it does going down. Only the velocity reverses. It follows that collisions don’t carry any heat down since the speed distribution of the molecules coming down is the same as the speed distribution of the molecules going up at any level. The only effect of the acceleration of gravitation is to limit the maximum height achieved by individual molecules and thereby to create an exponential density profile.

Rug, it was bearings I was thinking of. Instead of having a short, ball bearing, bearing, one could have long roller bearings, in multiple sleeves, a worm gear to the gearbox, a second long roller bearings, in multiple sleeves, and counter weight.

My take is that it is somewhat a threat and a bit hyped as well. I think the latest findings are more moderate. In North America the threat is worst farther north and moderates as you head south. There are remedial actions to prepare. Likely we will get advance notice and shutting down grid would prevent major damage (not that it is not. Big deal to bring it back up).

Jim,

You argument is based on the assumption that the sum of the potential temperatures does not change in conduction. That’s directly equivalent to assuming that the total entropy does not change in conduction, but neither is true. Both the sum of the potential temperatures and the total entropy increases.

Jim

Consider a situation where the lower parcel is at the temperature T1 and the upper parcel of the same mass at lower temperature T2 < T1. Move some heat from the lower to the upper parcel by conduction. Their temperatures change by equal amounts, because the specific heats are equal. The potential temperature do, however, not change by the same amount, as that of the upper parcel changes more based on the formula of the potential temperature. When you do the full calculation, you see that also the entropy increases in this process of heat conduction.