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Entropy is a measure of energy availiable for work ? 
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#37
Dec2312, 09:58 AM

P: 741

Making an unsupported claim is against the rules of the forum. I neglected to provide references and links before in my previous links. Therefore, here are a few references and links that show how gradients of partial pressure created entropy. http://www.landfood.ubc.ca/soil200/components/air.htm “Diffusion  moving force is gradient of partial pressure of any constituent member of air to migrate from a zone of higher to lower pressure, even while air as a whole may remain stationary. In other words, through diffusion each gas moves in a direction determined by its own partial pressure.” http://www.wileyvch.de/books/sample/352731024X_c01.pdf “Momentum transfer arguments lead to the conclusion that for diffusion in a gas mixture the gradient of partial pressure should be regarded as the fundamental .driving force,. since that formulation remains valid even under nonisothermal conditions.” http://www.chem.ntnu.no/nonequilibri...etfilee173.pdf “The small magnitude of the gradient of partial pressure along the airways suggests that the first contribution of entropy production can be neglected in the simplified model.” http://books.google.com/books?id=rYI...ure%22&f=false “The rate of diffusion of a gas is proportional to the gradient of partial pressure…” http://books.google.com/books?id=1wA...ure%22&f=false “As the permeate pressure is decreased, there occurred an increase in the gradient of partial pressure or chemical potential across a dried, nonswollen layer. As a result, when the permeate components become easily vaporized, the flux or total amount of product is increased.” http://www.decompression.org/maiken/...Strategies.htm “The gradient of partial pressure across the bubble surface. G = T  Pb, where T is tissue tension and Pb is the pressure inside the bubble.” No link here. However, Sears and Zemansky is a a classic textbook on thermodynamics. The following pages describe the process of how when different gases mix. “Heat and Thermodynamics, an Intermediate Testbook – 6th edition” by Mark Zemansky and Richard Dittman, (Mcgraw Hill, 1979) pp 361363. 


#38
Dec2312, 10:21 AM

P: 5,462

Here is another situation for you to consider: Consider a salt or sugar solution a few degrees above freezing point in an open vessel under constant pressure P. Now add a cube of ice at freezing point, of just sufficient mass that the result in the vessel will be a more dilute solution at exactly freezing point. What is the entropy of mixing? 


#39
Dec2312, 12:04 PM

P: 789

Chemical potential gradients will also cause entropy production. 


#40
Dec2312, 12:43 PM

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P: 6,679

Consider two identical volumes and quantities of ideal chemically inert gas molecules, say He and Ne, and both are at the same temperature and pressure but are separated by a wall. If you remove the wall the gas molecules will mix. And you can wait forever and the molecules will not unmix so it is not reversible. Entropy will increase. AM 


#41
Dec2312, 03:33 PM

P: 741

http://books.google.com/books?id=1wA...ure%22&f=false “As the permeate pressure is decreased, there occurred an increase in the gradient of partial pressure or chemical potential across a dried, nonswollen layer. As a result, when the permeate components become easily vaporized, the flux or total amount of product is increased.” I understand that chemical potential and partial pressure aren't precisely the same thing for other than ideal gases and solutes. I am not trying to promote my own definition of partial pressure. However... The specific scenarios discussed in this thread involve ideal gases. So until we get away from ideal gases, chemical potential of a component and the partial pressure of a component can be discussed interchangeably. Furthermore, the chemical potential of a component generally increases with the partial pressure of a component even for components that are not ideal gases. 


#42
Dec2312, 11:14 PM

P: 18

Would it be correct to say that TS is the energy not available for doing useful work?
When you write down any thermodynamic potential, you have the TS term, but the other terms (like PV, [itex]\mu[/itex]N, HM, etc) are the "work terms", which tell you how much useful energy you can get out of your system (depending on the constraints). Can anyone comment on this? 


#43
Dec2312, 11:58 PM

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P: 6,679

When a thermodynamic process occurs that results in a heat flow Qh from temperature Th, heat flow Qc to temperature Tc and work output W = QhQc, the energy that is "unavailable to do work" (which is also known as the "lost work") is the difference between the maximum work that can be produced (ie. in a reversible process) for that heat flow Qh from Th to Tc and the work actually produced. The "lost work" is TcΔS. For a reversible process, ΔS = Qh/Th + Qc/Tc = 0 so Qc/Qh = Tc/Th. For an irreversible process, Qh/Th + Qc/Tc = ΔS > 0. So the reversible work is QhQc = Qh  Qh(Tc/Th) = Qh(1Tc/Th). For the irreversible process involving the same Qh, the actual work is QhQc'. The difference between the reversible work and the irreversible work (ie. the lost work) is: [tex]W_L = (Q_h  Q_c)  (Q_h  Q_c') = Q_h(1T_c/T_h)  (Q_h  Q_c')[/tex] [tex]= Q_h(T_c/T_h) + Q_c' = T_c(Q_h/T_h + Q_c'/T_c )= T_c(ΔS)[/tex] AM 


#44
Dec2412, 11:32 AM

P: 789




#45
Dec2412, 04:42 PM

P: 741

Of course, this leaves the problem of systems that are not isothermal. Entropy is created in the regions of space where the gradient of chemical potential is not zero. That is what you said. Someone else said that entropy is only created in places where the temperature has a nonzero potential. According to your formula, the two statements are not equivalent. In a region where both temperature and partial pressure is nonzero, it may be possible to find points where the chemical potential is zero. For instance, the temperature and the partial pressure can be pointing in opposite directions with equal magnitudes. My current question is: 1) What type of gradients cause the generation of entropy? However, entropy is still an intensive quantity. Therefore, entropy is created at specific points regardless of what gradient generates it. It has to be created in the region where that gradient is nonzero. Entropy acts like an indestructible fluid, where temperature is like the pressure of the entropy. It can be created in a particular spot by a gradient, although I am not sure precisely what type of gradient that is. I am trying to find out. I haven't found any references where the author spells it out. 


#46
Dec2412, 04:55 PM

P: 5,462




#47
Dec2412, 09:33 PM

P: 789

Regarding gradients producing entropy, I think there are other possibilities, like the friction of a piston doing work. The entropy is created at the points of contact between piston and cylinder and is added to the system. Energy added is T dS if you can assume the whole thing happens at a constant temperature. 


#48
Dec2512, 12:50 PM

P: 741

I apologize. I tried to correct the situation. In any case, you don't have to worry about it. 


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