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I'm currently taking a course of introduction to biophysics in college and we currently covered a subject called entropy (S). We did some maths based on the Carnot cycle and came up with the following formula for this state function:

$$\partial S = \partial Q /\partial T $$

However the professor later stated that this function we call entropy measures the ability of a system to do work. How exactly does $\partial Q /\partial T$ gives us that information??

I'm confused, can someone please explain that to me in layman's terms? I'm not a physicist.

Urb
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ArielK
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2 Answers2

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I'm confused, can someone please explain that to me in layman's terms? I'm not a physicist.

The mathematical aspects of entropy are probably beyond layman's terms. Insofar as the link provided by @Jonas, although it's good, i'm not sure how helpful it would be to a layman.

Probably the most intuitive explanation of the second law and entropy that most folks can understand is rooted in everyday experiences. It has to do with the natural direction of processes. For example we all know

  1. Heat only flows naturally (without help) from hot to cold objects and

  2. Rivers always flow down-hill

And one that you, a biophysics student can relate to:

  1. People always grow old

These are all examples of what we call irreversible processes (they don't naturally reverse). For each process, entropy is generated. But all of these processes obey the first law of thermodynamics, which is basically conservation of energy.

For example, if heat flowed naturally from a cold object to hot object, the heat lost by the cold object would equal the heat gained by the hot object and energy would be conserved. But we never observe this to happen.

If water flowed naturally up hill it would lose kinetic energy and gain gravitational potential energy and energy would be conserved. But we never observe this to happen.

As far as the third example is concerned, ask your teacher how the second law applies to it.

Scientists (Notably Clausius and Carnot) realized that there must be another law and property governing the direction of processes in addition to the law of conservation of energy. Enter the second law and entropy.

Now as regards to the definition of entropy, the proper form of the equation is

$$dS=\frac{\delta Q_{rev}}{T}$$

Which says that a differential change in the property called entropy equals a reversible transfer of heat $\delta Q$ divided by the temperature at which the transfer occurs.

Entropy is generated when the heat transfer is irreversible, i.e., when it occurs over a finite temperature difference. This entropy generation may result in the lost opportunity to do work. A mathematical explanation is needed to show how. Your teacher should be able to help.

Hope it helps.

Bob D
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  • "People always grow old ... they don't naturally reverse" - from a purely chemical perspective, without arbitrary attribution of object identities, I see people constantly being reversed in age. Worms eat dead flesh, that goes into plants, those are eaten, and then a human is again recast in the womb. What sort of reversibility would you otherwise have in mind? One where the worms assemble an elderly person, who eventually crawls back into a womb to be digested for nutrients? I think such grand claims of non-reversibility would need more specifics and substantiation. – Steve Jan 26 '21 at 12:19
  • I don't see your point. The objects identity is highly relevant to the example. There is no doubt that aging is an irreversible process. That's the point. – Bob D Jan 26 '21 at 13:17
  • Just because the baby eats the dead person’s flesh, doesn’t mean the dead person is getting younger. The point with “people always grow old naturally” is that DNA unravels and becomes more disorderly with time, and so does the human body. – Adam Rubinson Jan 26 '21 at 13:18
  • @AdamRubinson Thanks for that. This article seems to support your statement (though I confess I know little or nothing of the subject) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2134939/ – Bob D Jan 26 '21 at 13:28
  • @BobD, but the identity is only ascribed by human convention - like the "grandfather's axe". There is no physical reality to that aspect. That's why I think these sweeping claims about biological irreversibility should be substantiated in far more detail, or withdrawn. – Steve Jan 26 '21 at 14:00
  • @AdamRubinson, as I just said to Bob, the identities attributed are arbitrary and conventional (that's not to suggest they shouldn't exist, only that their applicability to physics is seriously questionable). DNA doesn't always unravel and become more disorderly - birth and evolution are prime counter-examples by which the age of the bodies which carry DNA can become younger or more orderly, unless you're asserting some sort of creationist argument (and that ought to be explicit here, not left implied). Primarily, I maintain that these sweeping claims need to be substantiated. – Steve Jan 26 '21 at 14:05
  • "That's why I think these sweeping claims about biological irreversibility should be substantiated in far more detail, or withdrawn". No one said anything about irreversibility. But DNA does tend to unravel with time. "DNA doesn't always unravel and become more disorderly". I'm no Biologist. But if you ask a Biologist or a medical doctor, they will tell you that it does. Maybe you don't believe them? I don't think entropy of DNA unravelling is the same as saying "there certainly aren't transhumanist processes that could halt or reverse the unravelling process". – Adam Rubinson Jan 26 '21 at 14:24
  • But those transhumanist processes, if they exist, aren't "natural" in the sense that they are artificial/man-made. That's what is being said here, I think. $$$$ "bodies which carry DNA can become younger". For example, ...? You're saying birth? Okay well assuming you're right that DNA doesn't unravel before birth (which I don't know is true), just define "DNA unravelling after birth" then... Also, what are you trying to say about evolution? – Adam Rubinson Jan 26 '21 at 14:37
  • @AdamRubinson, his answer literally says "These are all examples of what we call irreversible processes"! It's silly to say nobody mentioned irreversibility. And if you ask a real doctor, I think you'll find they can quite readily explain the re-ravelling of DNA - it's exactly what happens during cell division or conception. The claims being made here intersecting entropy and biological processes, are utter cod. – Steve Jan 26 '21 at 15:50
  • @AdamRubinson, and yes, I give the example of conception and birth as an example of how the "body" which carries the DNA can become younger than before. I concede usually the DNA is changed (forming a synthesis between that of mother and father), but it's perfectly possible to work from a pure clone. (1/2) – Steve Jan 26 '21 at 15:53
  • It may be worth mentioning in passing that people usually refer to the heat input from the Sun as being the prime driver of reversal activity, and that the Sun will eventually exhaust and the state of things will then (supposedly) be fixed, but then the whole question becomes cosmological. We certainly see new stars forming as well as old stars dying in the sky. If we keep our feet on the ground in relation to this question, then there is no conclusive evidence for "irreversibility", and contrary examples abound. (2/2) – Steve Jan 26 '21 at 16:03
  • Ye you’re right he did mention “irreversible processes”: I only skimmed the answer. I think you’re mistaking the wood for the trees with this DNA stuff. Just because DNA doesn’t unravel in some specific circumstances doesn’t mean is doesn’t unravel in general. It’s like saying, “Newton’s laws are false because relativity is true”. Yes that is actually correct, but we still use Newton’s Laws to this day to help understand concepts. – Adam Rubinson Jan 26 '21 at 16:05
  • @AdamRubinson, as I say, unless you're advancing a creationist argument, then there must be some natural mode by which DNA "ravels". I'd suggest very pedestrian examples of reproduction, show just one example of how DNA which begins inside a 30-year-old woman, ends up in a much younger body than before, and is thus rejuvenated in exactly the fashion Bob tells us is utterly impossible. The fact that it is not in the same body as before, doesn't mean that conventional identity of the body has any relevance to the physical process by which DNA is constantly undergoing a rejuvenating cycle. – Steve Jan 26 '21 at 16:58
  • " as I say, unless you're advancing a creationist argument, then there must be some natural mode by which DNA "ravels"." Sorry but that's absolute nonsense. I think you've lost me at this point, and I don't have time to argue further. – Adam Rubinson Jan 26 '21 at 17:03
  • @AdamRubinson, the logic is very simple: if the Earth didn't arrive fully formed, with DNA and all, then there must be some natural process by which it is created. Most of this entropy guff dates originally from the 18th century, before evolution and natural selection was even articulated. – Steve Jan 26 '21 at 17:42
  • I'm not arguing with someone who fails to understand basic logic by committing fallacies, after asserting "the logic is very simple", in a discussion where "logic" doesn't even matter. We should be discussing scientific theories accepted through consensus here. – Adam Rubinson Jan 26 '21 at 18:14
  • thanks @BobD that helped a lot, it's not my "teatcher" acctually, it's my professor, he is just not very patient with biology students, he assumes we have a deeper understanding of this things, but anyway thank you for the answer – ArielK Jan 27 '21 at 13:07
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A somewhat similar question answered by me may be helpful in this case (please read that up untill the equations, at least, and continue here).
Concluding comments (to the aforementioned answer) -
Loosely speaking from equation (1), the entropy of a system is proportional to the number of accessible quantum states (this is what entropy is!) → more the amount of (co-ordinate/momentum) space available, higher the entropy, higher the disorder (because there will be more choices available for a particular particle to settle into - so, "order" does not mean a well-arranged/ordered outer appearance but refers to the number of accessible quantum states in & , neither it is a relative term). Thus, a disordered state is simply more probable because by the very definition above there are more states available to be occupied - for eg., this essentially means a particular particle has higher probability to occupy that state which has higher frequency of occurence = eg. if a system has more spin-up (|↑⟩) states available than spin down states (|↓⟩), then the particle has higher probabilty to be spin-up rather than spin-down.

user263315
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