# Confusion regarding Kelvin-Plank statement of Second Law

1. Jun 1, 2014

### physicslover23

Hello there. New here.

I have read and tried to understand the Kelvin Plank statement of the second law.

Essentially, it would imply, it is impossible to convert a given quantity of heat completely to work.
Why is it so? I mean, what is the justification for this?

I am ready to accept that it's practically impossible (to "devise" a heat engine) to convert heat completely to work, due to technological aspects like friction can't be zero, dissipation effects cannot be completely nullified, but theoretically in the most ideal case, why is it impossible?

And I am not looking for explanations that include entropy, because entropy is a consequence of the second law.
That'd be a circular argument.

If I go by first law, change in internal energy = heat - work. Therefore, Work=IE + Heat.
For work=heat, we need change in internal energy to be zero.

Why is the change in internal energy not reversible?

That is, I supply a heat (Say Q) to a body. Temperature (hence internal energy) increases. I want to take away the supplied heat Q in the form of work, so that internal energy reverts back to original. Why is that impossible?

Last edited: Jun 1, 2014
2. Jun 1, 2014

### dauto

It is a law. It's taken from empirical observation, conclusions are drawn from it and compared to experiments which confirm the validity of the law. How do you justify Newton's 2nd law "F = ma"? May be the correct formula ought to be. F = m a2. Well, the law is assumed to be correct, conclusions are drawn from it and compared to experiments that confirm its validity. Here's is an example: if the 2nd law of thermodynamics (2nd lot) was not true it would be possible to design a system that would extract energy from the environment cooling it down (free refrigeration) and use the energy to produce work (free power). This kind of device is known as a perpetual motion machine of the second kind which is empirically known to be impossible.

3. Jun 1, 2014

### physicslover23

I think experimental validation of laws are limited to only laws that are positive statements. If the law is stating an impossibility, there is no guarantee of the experimental validation, is there? One can always argue that it is not possible till now, which from a pure logical point of view, does not imply it cannot be possible at some later time.

Newton's second law states of something happening to be like something.
Second law of thermodynamics states an impossibility of an event. How can you prove impossibility by experiment? Essentially, there have been no experiment to prove the impossibility.

4. Jun 1, 2014

### physicslover23

Is it impossible to construct a PPM (of second kind) because of any reasons other than technological reasons like dissipation, friction and other losses? What I mean is, is there any internal loss? If so, how and why is that form of energy not recoverable into work?

5. Jun 1, 2014

### dauto

There is no difference between a positive statement "Entropy always remain constant or increase" and a negative statement "entropy never decreases". That's not an important distinction. Your mistake is to think that experiments can prove physical laws. They cannot. Laws can be disproven but they cannot be proven. Either an experiment is inconsistent with a law disproving it, or it is consistent with the law in which case the law survives the test but is not proven. That's always the case, whether the law's statement is a positive or a negative one (whatever that means).

6. Jun 1, 2014

### physicslover23

But there must be some theoretical arguments in favour of the law. There must be some justification. If you don't know it, maybe someone else will answer.

7. Jun 1, 2014

### dauto

Yes, there are justifications based on entropy, but you ruled that out as a derived quantity. If you take that point of view than the 2nd lot is the primitive principle taken as true without any justification other than the fact that it is born by experimental observation.

8. Jun 1, 2014

### physicslover23

I'm speaking from an extremely logical point of view. Is it then, justified to take a principle to be true without any justification?

Entropy is definitely derived from the second law itself, so logically it should be ruled out if you are seeking a justification of the law itself.

9. Jun 1, 2014

### DrStupid

It is not impossible but too unlikely for reproducible experimental observations.

It can be tested by experimental observations or derived from statistical mechanics. But I'm afraid such a derivation could be beyond the bounds of this forum.

Or vice versa. dS>=0 is just another wording of the second law.

10. Jun 1, 2014

### dauto

It is possible to take the non-decreasing entropy as the starting principle. From that point of view Kelvin's statement is a derived principle. Either way there will always going to be an statement that is taken as a principle and ultimately the justification for the principle is experimental consistency with experimental observation. That's always true for any physical principle. Physics is an empirical science.

11. Jun 1, 2014

### WannabeNewton

It's a straightforward consequence of statistical mechanics and every book on the subject will derive it so take your pick; my favorite is "Fundamentals of Statistical and Thermal Physics"-Reif.

But statistical mechanics has its share of fundamental postulates too so you seem to be wanting to go down a never-ending road.

12. Jun 1, 2014

### physicslover23

Thanks for all the replies.

Well, when entropy increases, the disorder increases in the sense that we do not KNOW the current (or final) arrangement. If we do not KNOW the current / final arrangement, it's impossible for us to revert the system back to the initial order. Thus entropy can only increase or remain constant and it is never possible to take it back to a previous order.

That's the best justification I could find.

Is my understanding correct?

13. Jun 1, 2014

### WannabeNewton

I don't quite think that's correct. Note that at no point in statistical mechanics do we ever completely know the current or final arrangement of a system, if by "arrangement" one means the microstate of the system. We only know with certainly the macrostate; the possible microstates are only given probabilistically by the distribution function for a given ensemble (e.g. Boltzmann distribution for the canonical ensemble). Even if a process is reversible, so that the entropy doesn't change between the two equilibrium states, we still do not know with certainty the current or final arrangement of the system, again if arrangement refers to the microstate. As already mentioned, statistical mechanics only tells us how to predict with certainty the macrostate of a system at equilibrium and the probability of it being in an associated microstate of that macrostate. This is not peculiar to irreversible processes.

The justification of the second law of thermodynamics using statistical mechanics does require just a tiny bit of careful argument. I don't think a forum post could fully do it justice.

You could take a look at Reif, who provides a very careful argument for it, but if you don't have access to it then Kardar also provides a good justification of it in chapter 4 of his text "Statistical Physics of Particles", which you can find in lecture note form here: http://ocw.mit.edu/courses/physics/8-333-statistical-mechanics-i-statistical-mechanics-of-particles-fall-2007/lecture-notes/ [Broken]. In particular see http://ocw.mit.edu/courses/physics/8-333-statistical-mechanics-i-statistical-mechanics-of-particles-fall-2007/lecture-notes/lec12.pdf [Broken]

Last edited by a moderator: May 6, 2017
14. Jun 1, 2014

### verty

I think this is somewhat analogous to the following situation. Suppose I strike a snooker ball and it strikes a second ball perfectly in the center. The first ball stops dead and the second ball has the same speed that the original ball had. But now I ask, is it possible for the first ball to strike the second and deform it without moving it? What I mean is, supposing there is no friction, there are just the two balls, why is it impossible for the second ball to convert all the energy into deformation? The answer is, it doesn't work that way, experiment shows that it doesn't happen.

Now compare it to the situation of removing heat from a body. I can introduce a cooler medium so that the heat will be transferred into the second medium. Perhaps that is a bimetal strip which when heated operates a thermostat. But why is it impossible for that bimetal strip to remain at the same temperature and convert all the energy into bending? Perhaps this is a silly comparison but I just don't see how you could come up with a way for the heat to be converted entirely. If there is no change in temperature, surely there can be no work done. Pressure couldn't increase, this type of bending couldn't happen, how could work be done?

15. Jun 1, 2014

### Philip Wood

The second law is suggested - I claim no more than this - by very simple thought experiments with an ideal gas. You'll find it impossible to draw on a p–V diagram a cycle in which heat taken in at one temperature is turned into work without 'excretion' of some heat at a lower temperature.

I'm NOT saying that the Kelvin-Planck law can be derived in this way. The restriction to an ideal gas, and the inadequate consideration given to the concept of temperature are enough to preclude any idea of this as a derivation.

But at least such thought experiments suggest the K-P law. As other posters have pointed out, once the law has been suggested, it can be treated as a hypothesis, and its practical consequences deduced – and tested. As Clausius and others showed, its consequences include the existence of the entropy function, and all sorts of testable relationships can be deduced from its existence.

16. Jun 3, 2014

### Useful nucleus

I'm not aware of any rigorous proof of the 2nd law. Even Kardar's notes posted above are not giving a derivation starting from statistical mechanics. Simply it tries to show consistency between the consequences of the postulates of statistical mechanics and the 2nd law.

The original poster does not like the Kelvin statement as it is stated in a negative sense. It is easy to show that it is equivalent to Clausius statement (See Kardar lecture 2 for a proof). Clausius statement is more intuitive to contemplate upon.

17. Jun 4, 2014

### Delta²

Has been proved any upper bound for the efficiency of the heat to work conversion? If not then as technology advances we can make conversions with efficiency 100%-a where a>0 can be as small as we want(=the technology allow us) but cannot become zero.

18. Jun 4, 2014

### stevendaryl

Staff Emeritus
Well, to see that this rule is at least plausibly true, note that the way that work can be extracted from heat is by moving heat from a hot object to a cold object.

Let me give an analogy: Water has a tendency to flow from high elevation to low elevation. A waterwheel can be used to extract work from flowing water as it flows. In this way of using a waterwheel, it can be a generator for electricity. It can also be used in reverse: if we add work to the waterwheel to make it turn in the opposite direction, we can make water flow in the opposite of its natural direction. In that way of using a waterwheel, it can be a pump.

Heat analogously has a tendency to flow from hot objects to cold objects. In analogy with a waterwheel, we could build a heat engine (this is the way that old steam engines worked) to extract work when heat flows. A similar design can be used in reverse: You add work to make the engine work to make heat flow in the opposite direction, from cold objects to hot objects. In this latter way of using the engine, it acts as a refrigerator: making cold things even colder.

So to convert heat into work, you have to allow that heat to flow in the natural direction, which is toward something colder. To convert the heat completely into work, you need to allow that heat to flow to something at the coldest possible temperature, which is absolute zero (-273 Celsius). So our ability to extract heat depends on our ability to get a reservoir of some substance to absolute zero. But there is no way to get to absolute zero.