Heat engine that violates Second law of thermodynamics?

[Amin2014]

What does the P-V diagram for a cycle that violates the Kelvin Planck statement of the second law of thermodynamics look like?

Would you say we cannot draw such a diagram BECAUSE of the second law?

 

[Andrew Mason]

What does the P-V diagram for a cycle that violates the Kelvin Planck statement of the second law of thermodynamics look like?

Would you say we cannot draw such a diagram BECAUSE of the second law?

If the PV diagram is going to represent the behaviour of a fixed quantity (mass) of an ideal gas, then PV/RT has to be constant at all times. So long as your graph obeys that constraint you can graph any kind of PV cycle you want.

However, keep in mind that PV diagram does not describe the state of the surroundings. The kind of cycle the graph represents (eg. engine cycle or a refrigeration cycle) is determined by the laws of thermodynamics. So, for example if you draw a horizontal line (a constant P process), T has to increase as volume increases. For example, if T increases as V increases, there has to be heat flow into the gas. In order to have heat flow into the gas, you cannot have the surroundings at a temperature lower than T.

AM

 

[Amin2014]

So long as your graph obeys that constraint you can graph any kind of PV cycle you want.
AM

So could you provide an example of a cycle that violates the Kelvin-Planck statement?

 

[Andrew Mason]

So could you provide an example of a cycle that violates the Kelvin-Planck statement?

Any cycle can occur if you have the right conditions in the surroundings. But the PV diagram for the working gas during the cycle does not show the state of the surroundings. So just drawing a PV diagram does not tell you whether the cycle violates the laws of thermodynamics.

It is the state of the surroundings, for example, that determines whether heat flow into the gas occurs on an isobaric expansion. If the state of the surroundings are not right (i.e. the temperature of surroundings is lower than temperature of the gas) heat flow into the gas will not occur and the isobaric expansion will not occur.

AM

 

[Amin2014]

Any cycle can occur if you have the right conditions in the surroundings.

I don't get this, the second law explicitly prohibits some cycles from occurring.

But the PV diagram for the working gas during the cycle does not show the state of the surroundings. So just drawing a PV diagram does not tell you whether the cycle violates the laws of thermodynamics.

Can you give a PV diagram along with the state of the surroundings during each step, and show how it violates the second law?

 

[mfb]

I don't get this, the second law explicitly prohibits some cycles from occurring.

It prohibits cycles in the whole system (under some conditions), your gas can still make cycles.

Can you give a PV diagram along with the state of the surroundings during each step, and show how it violates the second law?

As mentioned, a PV diagram of your gas cannot violate the second law. Only the whole system could do that.

 

[Amin2014]

It prohibits cycles in the whole system (under some conditions), your gas can still make cycles.
As mentioned, a PV diagram of your gas cannot violate the second law. Only the whole system could do that.

I don't get your point. Why can't you just state the details of each step alongside the PV diagram of the supposed device/engine that violates the second law and show that it violates the second law? Or show that the overall process violates the second law. I couldn't come up with any such diagrams without introducing non PV work.

A device (system), plus a single heat reservoir, the system undergoes a cycle (i.e. returns to its initial state), while converting all the heat provided by that single reservoir into useful work. To my understanding, this is precisely what the second law prohibits, no?

 

[Amin2014]

Are you guys saying that it is not necessary for the system to return to its initial state for it to count as a cycle?

 

[mfb]

I don't get your point. Why can't you just state the details of each step alongside the PV diagram of the supposed device/engine that violates the second law and show that it violates the second law?

If you add more data to the diagram, this is possible, sure, but then it is not a normal PV diagram any more.

Or show that the overall process violates the second law.

That is hard because it cannot do that (exactly due to this law).

A device (system), plus a single heat reservoir, the system undergoes a cycle (i.e. returns to its initial state), while converting all the heat provided by that single reservoir into useful work. To my understanding, this is precisely what the second law prohibits, no?

Right, this is forbidden.

Are you guys saying that it is not necessary for the system to return to its initial state for it to count as a cycle?

Not the whole system, right.

 

[Amin2014]

If you add more data to the diagram, this is possible, sure, but then it is not a normal PV diagram any more.

So could you show me one such diagram (along with the additional details) that violates the second law? A diagram I could point to and say: "Aha! So this is the (forbidden) cycle Lord Kelvin's talking about"

 

[Andrew Mason]

A device (system), plus a single heat reservoir, the system undergoes a cycle (i.e. returns to its initial state), while converting all the heat provided by that single reservoir into useful work. To my understanding, this is precisely what the second law prohibits, no?

A Carnot engine operating between some finite temperature and a cold reservoir that was arbitrarily close to absolute zero would approach 100% efficiency. That would not violate the first or second laws. Since one can never reach absolute zero (third law) you could never get an actual 100% efficient Carnot engine even in theory.

So could you show me one such diagram (along with the additional details) that violates the second law? A diagram I could point to and say: "Aha! So this is the (forbidden) cycle Lord Kelvin's talking about"

The diagram would have to show more than just the P and V of the working substance. It would have to provide details of the state of the surroundings during the cycle.

AM

 

[stevmg]

Any heat engine that is more efficient than Sadi Carnot's cycle inherently requires
1). Either a permanent T1 (elevated heat source by the environment, not from the fuel source(

Or

2). A mythical T2 (heat sink temperature) below the ambient environmental temperature by some magical means

No such animal exists. The Carnot cycle is a closed system. This brings the engine back to initial starting conditions. Any other system violates the return to starting conditions and requires a permanent discordance between starting point and ending point which allows energy to flow high energy level to low energy level (T1 down to T2 or PaVa to PbVb). Carnot wasn't referring to that.

A simplistic example of such would be the PaVa - PbVb isotherm course in which heat energy is supplied along this isotherm and work by the system is done with 100% efficiency. Unfortunately that requires a permanent discordance in beginning and final states. Other than Niagara Falls or a volcano, this doesn't exist.

 

[stedwards]

What does the P-V diagram for a cycle that violates the Kelvin Planck statement of the second law of thermodynamics look like?

Why don't you provide some candidates? It's your question. It would be more to chew on than a lot of back and forth rhetoric going nowhere.

 

[stevmg]

@stedwards. It appears that Amin2014 doesn't know where to begin otherwise he/she wouldn't ask the question. It also appears that the real question is: is there a PV diagram that violates the Kelvin-Planck hypothesis?

Do you (stedwards) know of any such diagram? I am not a thermodynamics physicist but I think Carnot put that item to rest in the 1820s with his famous "parallelogram" heat cycle diagram which indirectly states the Second Law. Do you, or anyone out there, know of any potential PV diagram which would violate the Second Law? All other conjectures somehow assume either a hidden permanent heat source or a hidden persistent cold heat sink, far below environmental conditions.

 

[mfb]

This thread is half a year old. I suggest to let it rest unless Amin2014 comes back with follow-up questions.

 

[stevmg]

This thread is half a year old. I suggest to let it rest unless Amin2014 comes back with follow-up questions.

You DID answer the question earlier in the thread by, essentially stating that no PV diagram can violate the Second Law. Carnot proved that himself in the 1820s although he didn't know what the Second Law was.

 

[stedwards]

@stedwards. It appears that Amin2014 doesn't know where to begin otherwise he/she wouldn't ask the question. It also appears that the real question is: is there a PV diagram that violates the Kelvin-Planck hypothesis?

Do you (stedwards) know of any such diagram?

No, I don't. Please forgive me for being so contrite, previously.

 

[stevmg]

No, I don't. Please forgive me for being so contrite, previously.

Contrite? You don't have to be remorseful for anything.

There must be some proof out there that the Carnot parallelogram gives "the most for the least"'(the most efficient). My guess is that by drawing any other diagram that produces more output (higher efficiency) violates some basic thermodynamic premise. To wit, the Otto Cycle used by automobile buffs to prove higher efficiency in internal combustion engines is deficient in following thermodynamic principles in that their proponents ignore the return part of the heat engine cycle and posit a permanent unlimited cold heat sink and that the return part of the loop is ignored "nature's gift to man."

I think the molecular basis for this whole thing is that a theoretical molecular gas can expand while doing no work and not requiring heat to do so but to return (recmpress) the expanded gas back to its original state requires work, i. e., increasing entropy.