At this point we both acknowledge that the entropy of the isothermal gas column is greater than the entropy
of the isentropic gas column.
Not exact matches
O'Gorman, P. A., N. Lamquin, T. Schneider, and M. S. Singh, 2011: The relative humidity in an
isentropic advection - condensation model: Limited poleward influence and properties
of subtropical minima.
It is Roy who either needs to make even just one comment on his own thread to either admit he's wrong, or prove all
of us at PSI are wrong in some way, perhaps because the Second Law
of Thermodynamics would not somehow lead to
isentropic conditions, rather than isothermal in a vertical plane.
Yang, H. and Pierrehumbert, R. T. 1994: Production
of dry air by
isentropic mixing.
But this favorite paper
of yours specifically starts part b by saying: b.
Isentropic profile Now, in Ball [1956, Eq.
The dry adiabatic lapse rate is derived several ways, each
of which assumes an
isentropic atmosphere.
The thought experiment
of Fig. 1 in top post being isothermal at equilibrium is wrong & shown irrefutably (by many published atmospheric thermodynamic physicists cited) to be non-isothermal,
isentropic in equilibrium by the correct algebraic steps to maximize entropy and reasonable experiments as posted above.
This change results in the column
of fluid being out
of thermodynamic equilibrium and results in an
isentropic profile defined by a temperature lapse rate.
If instead the vertical integral
of the potential temperature is kept fixed — as argued by several authors to be appropriate in the case
of convective mixing — an
isentropic profile results.
An
isentropic state is the state
of maximum entropy and will not separate into a state with a different potential temperature profile because that would have a lower entropy, given that total potential temperature has to be conserved when integrated over the mass in adiabatic processes.
If one could concede that the true equilibrium state may be
isentropic instead
of isothermal ``
entropy, conserving total enthalpy / energy equilibrium
of Fig. 1 is irrefutably proven non-isothermal,
isentropic by published atmospheric thermodynamic physicists as early as 1996, again in 1998, 2004 and 2010 including experiments validating their results.
And, folks, that Verkley part b constraint 3) is EXACTLY top post Fig. 1 for reasonable 80 %
of earth's atmosphere which leads the paper to irrefutably mathematically prove the thermo law consistent non-isothermal,
isentropic temperature profile for top post Fig. 1.
Condensation without supersaturation is essentially
isentropic as long as the droplets don't fall, but their descent under gravitation is neither
isentropic nor adiabatic, as they carry heat across the boundaries
of a parcel
of gas.
Radiative equilibrium does drive towards an isothermal state, but mixing goes towards an
isentropic state, which is a recognized term indicating constant potential temperature (also dry adiabatic) because the log
of potential temperature is basically the entropy in thermodynamic terms.
One part
of the approximate isentropy is that the level
of supersaturation is low, as condensation
of supersaturated vapor is not
isentropic.
In the
isentropic case the rate
of cooling can be calculated exactly, otherwise the cooling will be less.
That kind
of atmosphere is, however, not
isentropic or in thermodynamic equilibrium.
The continuity equations and the thermodynamic equations related to
isentropic processes
of rising air and condensation determine the whole process.
In this case I started be defining a rather idealized case
of uplift that's adiabatic and not far from
isentropic.