For the isothermal layer not to descend, there would need to be a balancing force to offset the expansion above the condensation layer.
As already said, the radiative heat transfer surface to air is the radiation of the surface absorbed by the air minus the radiation of the air absorbed by the surface: it would be exactly zero
for an isothermal atmosphere and is nearly zero for an opaque atmosphere (figure 6 - A).
Caballero supports isotropic velocities
for isothermal T only in the no gravity ideal gas column case.
My point was that Velasco dealt with the statistical mechanics at issue, and he came down strongly
for isothermal, in agreement with Dr. Brown.
PPS I trust you remember that Dr Brown (and I and all the other arguing
for an isothermal gas in this special situation recognize that a REAL atmosphere with GHGs radiating to space WILL have a vertical temperature gradient, but that this is a completely different situation.
I am still of two minds because there are several ways
for an isothermal column to be disrupted vertically: Is it hotter on top when there is no radiation into space or at the bottom where teh gas is compressed?
al. can say, view agrees with Verkley part a, just choose my constraints
for isothermal.
«Caballero supports isotropic velocities
for isothermal T only in the no gravity ideal gas column case (in 2.17).
Again, 2.17 is
for the isothermal no gravity isotropic velocity case, you can not use Caballero here to support dT / dz = 0 isothermal gas column in a gravity field.
I do think that they can count as evidence
for isothermal equilibrium — they certainly aren't evidence against it — just perhaps not conclusive under the circumstances.
At the minimum, it seems
for an isothermal T field conclusion, Fig. 1 in the top post must be modified to show at the top and bottom of the column: ``... may perform work on the atmosphere air above and below the column.
The S
for isothermal will be less than the non-isothermal field.
Tim — Correct, the S
for isothermal will be less than S for a non-isothermal field which is maximum S.
My posts here have been about the lack of experimental evidence
for isothermal / adiabatic distribution.
Still, I have no problem with you not considering the Uranium centrifuges as not being conclusive evidence
for isothermal equilibrium.
No, they do not have perfect insulation in part
a for isothermal case, they allow work across the insulation — read again the statement in Verkley Fig. 1 as I quoted, their air column is different than Fig. 1 top post.
It is amazing that such accurate predictions can be obtained from the two simple laws, constant
for an isothermal gas, and constant for an adiabatic gas.
The Venus surface would not be hot if there were a propensity
for isothermal conditions in a gravitational field, as Roy Spencer claimed.
The formula So * (1 - albedo) * 0.25 = sigma T ^ 4 is valid only
for an isothermal blackbody «bare rock» in space.
The 2 - layer equilibrium relationship Ta = 0.84 Tg, which is valid
for an isothermal gray absorbing layer above a Planck emitting ground, when applied to multiple layers is valid only when the layers are either totally transparent or totally opaque.
Not exact matches
The temperature dependence of the
isothermal compressibility and correlation length extracted from x-ray scattering functions showed maxima at 229 K
for H2O and 233 K
for D2O, rather than diverging to infinity.
They then used a portable
isothermal amplification device — which could be used
for point - of - care testing — to identify Zika RNA.
A novel diagnostic method
for malaria using loop - mediated
isothermal amplification (LAMP) and MinION ™ nanopore sequencer
An parcel means that the medium is small enough to be
isothermal and in local thermodynamic equilibrium (which then ensures that the population of thermodynamic molecular energy levels will be set by molecular collisions at the local atmospheric temperature), but the parcel is also large enough to contain a large enough sample of molecules to represent a statistically significant mass of air
for thermodynamics to apply.
Since the 155 W / m2 GHE is the GHE forcing based on the present climate (in the sense that removing all GH agents (only their LW opacity, keeping solar radiation properties constant) results in a forcing of -155 W / m2 at TOA
for the present climate, and we know that without any GHE, in the
isothermal blackbody surface approximation, the temperature will fall approximately 33 K without any non-Planck feedbacks), it can be compared to smaller climate forcings made in the context of the present climate (such as a doubling CO2.)
In Kiehl and Trenberth 1997, they find a 155 W / m2 total greenhouse effect
for approximately present - day Earth conditions (among the approximations: surface is a perfect (
isothermal **) blackbody, and the use a representative 1 - dimensional atmospheric column (instead of seperate calculations
for each location over the globe at each time over the course of a period of time sufficient to describe a climatic state — but note righthand side of p. 200, just past halfway down the column)... a few other things).
Re 423 Chris G — whether the effect saturates at a given density depends on the way the temperature is distributed; if the temperature from TOA downward is
isothermal for a sufficient thickness, than the effect could be saturated at TOA (if starting from a large enough optical thickness per unit atmospheric mass path, a change in the density of the gas / etc that contributes optical thickness would then have little to no effect on the flux at TOA, which is what is meant by saturation.
But when optical thickness gets to a significant value (such that the overall spatial temperature variation occurs on a spatial scale comparable to a unit of optical thickness), each successive increment tends to have a smaller effect — when optical thickness is very large relative to the spatial scale of temperature variation, the flux at some location approaches the blackbody value
for the temperature at that location, because the distances photons can travel from where they are emitted becomes so small that everything «within view» becomes nearly
isothermal.
The OLR will not generally be isotropic unless the whole atmosphere is optically quite thin (entirely within the skin layer except
for the troposphere) or if an optically thick upper portion is
isothermal.
That has led some to propose that after a while such an atmosphere becomes «
isothermal» (the same temperature from top to bottom) at the same temperature as the surface save
for a shallow layer in contact with the ground which can warm and cool conductively with the ground as sunlight comes and goes.
From these postulates, one can derive a rigorous expression
for the climate sensitivity of any system bounded by two
isothermal surfaces through which only energy enters and departs.
Take the steady - state
isothermal flow of an incompressible fluid through a straight round pipe and
for which a known flow rate is imposed.
Because of the higher thermal mass, in both cases, the energy source can be approximately as effectively
isothermal for a longer time period.
Note that it is essential
for the greenhouse effect that the temperature of the lower atmosphere is not constant (
isothermal) but decreases with height.
Pretend the earth can be approximated by a 1 - d model
for earth, where the earth is treated like an
isothermal body (say a nice copper sphere) with some sort of atmoshpere.
Obviously if they think there would be
isothermal conditions, then they are never going to be able to explain why a region of the surface covered with thick clouds
for several days and nights, still warms by day and cools by night.
In the end, you will see why, and how, thermal equilibrium must be
isothermal and how all of your efforts to argue that it is not each leads to a straightforward violation of the second law of thermodynamics (as well as not being the actual solution to the problem in thermodynamics or statistical mechanics, correctly done, as has been known
for well over 100 years).
They do come to the same conclusion; they quite clearly show — and state — that,
for any macroscopic system, canonic or microcanonic — the sort of system we are actually interested in here — the result is
isothermal, as it should be.
7.48 in B&A) provides some clues to me as to root cause why you are stuck on manifestly assuming the incorrect
isothermal equilibrium solution
for Fig. 1 where you disagree with all 3 expert references I cite — which show their algebra.
The fact that air in fact conducts heat just like the silver, and that if you wait
for equilibrium — whether or not it actually takes a very long time on a human scale to get there — the equilibrium reached will be
isothermal or violate the second law, in particular by manifestly not being the maximum entropy state of the system.
The questions that remain are: Is
isothermal state the lowest energy state
for a compressible gas in a gravity field?
Because in the back of my mind I had
for some time wanted a satisfactory basis
for deciding between the
isothermal and dry - adiabatic - lapse - rate schools of thought.
Geez, Verkely seems to find both non-
isothermal AND
isothermal T fields depending on constraints
for top post Fig. 1.
Poster Rodrigo Caballero is writing about the
isothermal case when work is allowed across the top and bottom control volume which is not the case
for Fig. 1 in the top post.
2004» and by my read, they consider that applying the two constraints of constant mass and constant energy (or enthalpy) to the fluid will result in an
isothermal profile
for the fluid in thermodynamic equilibrium.
For Velasco to support paradox resolving to
isothermal column, this equation would have collapsed to KE = TE meaning molecular velocities are isotropic in the presence of gravity thus
isothermal.
It might take years
for the atmosphere to relax to
isothermal.
Bounded by a black upper surface, it won't even take long
for the gas to become
isothermal at reasonable temperatures even if it is started with a DALR or other thermal gradient.
For any to refute me conjecture, just explain in math how these two actual examples do exist as they are while would also transform to a totally
isothermal state if all radiation is removed: Venus: 8.26 °C / km DALR — 5W / m2 constant input at the base — 65W / m2 total Earth: 9.8 °C / km DALR — 160 - 640W / m2 constant input at the base — 240 - 960W / m2 total
For a thought experiment, lets suppose we could let the earth stabilize to an absolutely
isothermal condition, then «turn on» the weather, sun etc. to let the drivers begin to drive the system.