Carnot engine with a hot negative and a cold positive temperatureNote also the unusual behavior of a reversible
Work Out/Hot Heat In = 1 + |Tpositive/Tnegative| > 1
This seems to be related - heat from both reservoirs performs useful work. It seems obvious to me that this should have implications for nanomotors.OK
Negative Specific Heat in Astronomy, Physics and Chemistry
Institute of Astronomy, University of Cambridge, CB3 0HA and Clare College, Senior Fellow visiting The Queen’s University, Belfast. BT7 1NN
"Starting from Antonov’s discovery that there is no maximum to the entropy of a gravitating system of point particles at fixed energy in a spherical box if the density contrast between centre and edge exceeds 709, we review progress in the understanding of gravitational thermodynamics.
We pinpoint the error in the proof that all systems have positive specific heat and say when it can occur. We discuss the development of the thermal runaway in both the gravothermal catastrophe and its inverse.
The energy range over which microcanonical ensembles have negative heat capacity is replaced by a first order phase transition in the corre- sponding canonical ensembles. We conjecture that all first order phase transitions may be viewed as caused by negative heat capacities of units within them.
We find such units in the theory of ionisation, chemical dissociation and in the Van der Waals gas so these concepts are applicable outside the realm of stars, star clusters and black holes.
1. Two negative CV systems in thermal contact do not attain thermal equilibrium – one gets hotter and hotter by losing energy, the other gets for ever colder by gaining energy. Thus negative CV systems can not be divided into independent parts each with negative CV ; so negative CV systems are NEVER extensive.
2. A negative CV system can not achieve thermal equilibrium with a large heat bath. Any fluctuation that, e.g., makes it temporary energy too high will make its temporary temperature too low and the heat flow into it will drive it to ever lower temperatures and higher energies.
3. A negative CV system can achieve a stable equilibrium in contact with a positive CV system provided that their combined heat capacity is negative. ...
Notice that this stability is lost as soon as Plus has the same |CV | as Minus; i.e., when their combined heat capacity reaches zero from below."
On Dec 27, 2010, at 9:23 PM, JACK SARFATTI wrote:
Yes, I already knew that the specific heat is negative for the bh and those stars and thought about mentioning it, but how does that fit in? I am missing something here in connecting the dots.
On Dec 27, 2010, at 7:55 PM, Raymond Chiao wrote:
Yes, "creating the temperature difference is ok so long as the total entropy is increasing to compensate". However, Unruh reminded me recently that the specific heat of a black hole is negative, as Lynden-Bell first pointed out is the case for ordinary, non-relativistic self-gravitating stars. See Ref. ; see look up under "negative specific heat" using Google.
of course since the area of the right BH is increasing the total entropy of the system is not decreasing so I am reminded of a refrigerator - creating the temperature difference is ok so long as the total entropy is increasing to compensate?
On Dec 27, 2010, at 11:43 AM, Raymond Chiao wrote:
"Jack, excellent question! You are right that the time scales for the fluctuations could be different for fast fluctuations, such as the fluctuations due to fluctuating photon number in the photon flow from the left to the right cavities, and for the slow, secular changes (perhaps one shouldn't use the word "fluctuations" in this case) in the masses of the two BH's due to a steady flow of radiant energy from the left BH to the right BH. The fast fluctuations will indeed average out and "stabilize", but not the slow, secular changes. However, like in the case of the Jeans instability, one doesn't need to specify the nature of the fluctuation that initiates the instability. The secular instability will always dominate over long time scales. " --Ray
if the time scale of the fluctuations is much shorter than the time scale of the instability won't it stabilize? - statistically average out if a fluctuation happens on the left BH a canceling fluctuation happens on the right BH etc? I wonder if the ratio of the time scale of the fluctuations to the time scale of the instability is independent of the mass of the BH?