Duncan s' Paradox

[Gabriele]

Its important to remember that a process that gets cold or takes energy from the environment doesn't imply a violation of the second law at all. This is a very common rookie mistake.

Which are these cases?

[pomodoro]

The Karpen pile is a classic example in the OU community and any other endothermic process doing work. Another is the  expansion of a liquefied gas through a turbine to generate more work than used to compress it in the first place after  allowing it to cool to room temperature before expanding. Lots of heat is taken from the environment and the gas cylinder greatly cools.

The second law is often stated in plain language, in such terms as "Water can only flow uphill", "The amount of work obtained from a fixed quantity of heat given up by a heat engine operating in a reversible cycle between two temperatures approaches zero  as the temperature difference approaches zero",  to the more descriptive statement by Lord Kelvin  "it is impossible to construct an engine, which is operating in a cycle produces no other effect except to external heat from a single reservoir and do equivalent amount of work. There are literally dozens of similar definitions, which lead to confusion.

However, the definitive Second law definition is that for a process to be possible, without externally applied work, that is, spontaneously, the total entropy must have increased.  This is the ultimate definition of the second law.  The total Entropy is the Entropy of the system + Entropy of the environment caused by the process.  Or ΔS_total > 0   ie: ΔS_environment +ΔS_system > 0.  ΔS means the change in entropy.


Without boring readers, it can be shown from the Gibbs free energy equation that  ΔS_environment = -ΔH_system/T.   ΔH is the change in enthaply from the process, which is the Energy difference plus any work from changes in volume, which amounts to pΔV work at constant pressure (air pressure). Note here that any other work that is not due to pΔV needs to be added here, lets call this W.  W is zero most of the time because these formulas only work at constant temperature, and heat engines need a change in temperature ΔT,  however if a system can perform work, which doesn't require a ΔT, (after all pΔV is work, but requires no ΔT) then it need to be added.  This W being greater than zero in the real world is not common as we know.
So we now have:

ΔStotal= -(ΔHsystem+W)/T + ΔSsystem

Remembering that if ΔStotal >0 the process can spontaneously go ahead, and also remembering that a ΔH that is positive means an endothermic, or cooling process, we can plainly see that as long as ΔSsystem is quite large, we can remove heat from the environment (ΔHsystem+W), possibly get some work, W and still have an entropy change that is positive.  In other words, heat is removed from the environment, but work is done.  Another classic example, without any work though, is the dissolution of ammonium nitrate. The water gets very cold, endothermic, but the process is still covered by the second law, because the ΔSsystem is huge. The trick for 'OU' is to discover a process capable of doing work without a  temperature difference.

[Gabriele]

It is more than a couple of years i'm theoretically experiment systems seems to violate 2nd law of thermodynamic. The system is a contaniner with a low heat capacity gas at very low pression at the vapour pressure point at the base. It is clear that 1 meter up from the base the gas pressure is a little lower. From my computations the theoric energy needed to liquefy with an heatpump the gas at 1m of height is about an half the energy obtained let falling the liquid for 1m. It seems less dense the gas is,more is the difference from Ein and Eou

This is the calculator i use to find variables in pressure and temperature https://www.irc.wisc.edu/properties/

But can be a systematic error

[dieter]

Well, whether it violates the 2nd law or not, I let judge the physicists, and they obviously seem to think so.

Also, an aperatus having one surface with a tendency to disintegrate H2 and an other surface with a tendency to recombine 2H is not operating in the microwatt range when you consider the active area is only 2D, but multiplied by a third dimension becomes rather substancial. Esp. considering the molecular expansion forces of H2/2H in a confined space.

Alternatively, considering a permanent temperature diffrence that can easily drive a stirling engine with no fuel whatsoever.