How to Beat the Second Law

I like this statement for the Second Law of Thermodynamicsâ€"
   "You can't fool Mother Nature."

That seems rather obvious, don't you think?  And this very certainty is why the Second Law is called a "law."  Now, here is what I mean by saying that Mother Nature can't be fooled.  Nature dictates that rocks roll down hill.  This is a one-way process.  No matter how much you talk to it, a rock will NOT roll up hill.  Of course, you can carry it up-hill if you want, but you should eat a good breakfast because some work will be required.  There are many other examples of things going only one way in nature.  Water flows down-stream.  Heat flows "down" from a higher temperature to a lower temperature.  The reverse processes NEVER happen, although you might create the appearance of it by putting in work of some kind.

Of course our interest here is in getting as much "free energy" as we can, or at least not paying any more than we have to.  As I see it, energy only comes in two kindsâ€"

   (1)  Stuff we call "work."  This can do things for us.
   (2)  Heat, what we often end up with if we do some work.

As far as I can tell, any form of energy that isn't heat is a kind of work.  So, sunlight for example is work.  A magnetic field is work.  As a general principle, one kind of work can be exchanged for another kind at little or no cost if we are careful.  But if you aren't careful, some of the work goes to heat, and eventually it all ends up that way.  Nature will let us change our more useful, orderly "work" into heat any time we want.  Or, it is only too happy to do it for us.  BUT we are not allowed to simply exchange heat for work.  Again, this is a one-way process, and really no different than others mentioned before.  When a rock rolls down hill, it loses gravitational potential (work) and converts that energy into heat.  But once the rock has expended its work, it can't get it back again.

All of these processes that nature urges in one direction we call "spontaneous."  Heat will move spontaneously from a place of high temperature to another place at a lower temperature, if there is a path.  So we see that heat at a high temperature has more possibilities for use.  And, heat at a low temperature is more "useless."  A good measure for that is Q /T where Q is the amount of heat added and T is the absolute temperature at which you add the heat.  This is called the entropy change.  Besides a name, it is also given a symbol, Î"Sâ€"

   Î"S  =  Q /T

As T gets smaller, the entropy change gets bigger, so moving heat from a high temperature to a low temperature increases entropy.  Or, changing work to heat will also increase entropy by creating new heat.  So, without going into all the details about why Q/T is the right measure, we can see that whenever a process happens, there is a positive entropy change, or at least it isn't negative.

Now, let's write a general equation for processes involving energy changes.  Let's say that the state before the change is "1" and the condition after is "2".  Some of the heat has been exchanged for work or vice-versaâ€"

   W₁ + Q₁ = W₂ + Q₂

What we have here is a statement of the First Law of Thermodynamics, that the total amount of energy never changes in a process, if you are careful to account for all of the energy.  In order for this process to occur, we will say that the entropy increases, so the entropy after is greater than the entropy before.  (This is a form of the Second Law)â€"

   Q₂ /T₂  > Q₁ /T₁

Notice that so far, T₁ can be either bigger or smaller than T₂.  Here are some conclusions to be drawnâ€"

   If T₁ > T₂, then Q₁ may be greater than Q₂, and then W₂ > W₁
   If T₁ < T₂, then Q₂ must be greater than Q₁, and W₁ > W₂

I will leave it to you to think through these situations and see that the conclusions follow logically.  If W₁ = 0 and T₁ > T₂, then you have the case of an engine.  If W₂ = 0 and
T₁ < T₂, then you have the case of a refrigerator or a heat pump.  Let's go ahead and look at the case of an engine, where you start with just heat, so W₁ = 0 â€"

   Q₁ = W₂ + Q₂   where T₁ > T₂ and Q₁ is greater than Q₂

And in order for this engine to work, I know that the entropy must increase, in other words, Q₂ /T₂  > Q₁ /T₁.  I will rearrange these two expressions, remembering that the efficiency of the engine is defined as the work W₂ divided by the heat put in from the fuelâ€"

   W₂ /Q₁ = 1 â€" Q₂ /Q₁
   1  > Q₂ /Q₁ > T₂ /T₁

Let's call W₂ /Q₁ = Eff, because that's the efficiency of the engine.  It is something positive, but less than one.  Combining these expressions, we get the Carnot formulaâ€"

   Eff  <  1 â€" T₂ /T₁

All engines that work have to satisfy this formula.  In some cases, we could have some complication about defining what the temperatures are, and then you might need to modify the formula some.  Whatever the situation is, you can be assured that entropy increases when you run the engine or it flat won't work.  If you have a "perfect, reversible" engine, then theoretically, you could use an equal sign in this formula.  And, that is the Carnot limit for an engine's maximum efficiency.

What's that?â€"you say I promised to tell you how to "beat the Second Law"?  Oh, yes, I did, didn't I.  Okay.

Let's look at how a typical engine works.  A fuel is burned, and then the heat is used to power the engine.  There's the mistake, right there.  The fuel contained chemical energy.  Chemical energy is WORK.  Naturally, if you allow the chemical energy to be converted to heat, nature doesn't mind at all.  The entropy went way up right there. And then the engine turns around and tries to convert some of the energy back to work, with a substantial loss and a further increase in entropy, according to the Second Law.  If you don't want to be subject to the Second Law, then don't convert work into heat if you don't have to.  And, in principle, we know how to do that.  Chemical energy can be converted to another kind of work with much less inefficiency.  One way to do that is with an electrochemical cell.  The chemical energy goes directly to electrical energy, and if you do it right, you can keep as much as 90% of the work you started with.  No heat engine can match that.

There are some other ways to beat the Second Law of Thermodynamics, but let's save that story for another day.

Ernie Rogers

As one using thermographic tools I think I understand the 2nd law pretty well. So why is it Momma taught us to to hold the cast iron skillet with a rag while cooling it with cold water?

Naturally I didn't follow her advice the first few times.  Even if the handle is just warm to the touch you may wind up with burns.

Quote from: BEP on February 19, 2009, 01:18:40 PM
As one using thermographic tools I think I understand the 2nd law pretty well. So why is it Momma taught us to to hold the cast iron skillet with a rag while cooling it with cold water?

Naturally I didn't follow her advice the first few times.  Even if the handle is just warm to the touch you may wind up with burns.

Oh, yes, we can't fool your Momma either.

Ernie Rogers

Quote from: CARN0T on February 17, 2009, 02:01:00 AM
How to Beat the Second Law

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Let's look at how a typical engine works.  A fuel is burned, and then the heat is used to power the engine.  There's the mistake, right there.  The fuel contained chemical energy.  Chemical energy is WORK.  Naturally, if you allow the chemical energy to be converted to heat, nature doesn't mind at all.  The entropy went way up right there. And then the engine turns around and tries to convert some of the energy back to work, with a substantial loss and a further increase in entropy, according to the Second Law.  If you don't want to be subject to the Second Law, then don't convert work into heat if you don't have to.  And, in principle, we know how to do that.  Chemical energy can be converted to another kind of work with much less inefficiency.  One way to do that is with an electrochemical cell.  The chemical energy goes directly to electrical energy, and if you do it right, you can keep as much as 90% of the work you started with.  No heat engine can match that.

There are some other ways to beat the Second Law of Thermodynamics, but let's save that story for another day.

Ernie Rogers

The combustion engine works by burning fuel. Burning is a one way process, so the energy can't be reused to burn again - at least not in an instant.
To do work you actually does nothing at all. Moving an object from A to B does not cost anything. What is payed for is the friction between A and B.
When you start moving an object angular to gravity, you spent energy in accelerating, but you can get this energy back at retardation at point B.

The best way to do this, is to to use electricity and magnetism - an electric driven car. You decharge the battery when accelerating, and charge the battery when breaking. Along the way you loose some useful energy due to friction, but nevertheless, no net work is done by moving an object from A to B. The traditional thinking is that when you have accelerated an object, this spent potentional energy isn't stored anywhere - just lost as heat.

Maybe I didn't read yout post well enough

Br.

Vidar

Dear Carnot,

Please read my post subject Curled Ballistic Thermionics.

I have a number of professors and experts already in agreement.

As you know there is no proof of the 2nd Law.

I now claim there is a proof that the Lord Kelvin statement was a viewpoint and a half baked theory, not a law and it is now relegated to myth.

Phil H