An experiment against the second law of thermodynamics

[cianfa72]

TL;DR Summary

About the proposal of an experiment that at first glance violates the second law of thermodynamics

Hi, soppose we have a resistor at a given temperature T connected through a diode to a cell battery.

The voltage accross the resistor due to thermal noise should charge the cell converting termal energy into chemical energy without limits.

Does the above process violate the second law of thermodynamics ?

 

[russ_watters]

The voltage accross the resistor due to termal noise

That's not a thing.

Note: PF does not entertain discussion of Perpetual Motion machines or personal theories.

 

[cianfa72]

That's not a thing.

Note: PF does not entertain discussion of Perpetual Motion machines or personal theories.

No idea to entertain such a discussion. Mine is a simple question.

 

[russ_watters]

No idea to entertain such a discussion. Mine is a simple question.

What you describe is a perpetual motion machine. In any case, I answered the question. You seem to have a misunderstanding of what resistors are. Resistors don't drive current, they resist it.

 

[cianfa72]

Resistors don't drive current, they resist it.

Sorry, a real resistor can be modeled as an ideal resistor + a series thermal noise voltage source.

 

[russ_watters]

Sorry, a real resistor can be modeled as an ideal resistor + a series thermal noise voltage source.

Provide a source for this claim and a diagram of the circuit. I am pretty sure that what you are saying is not true as you intend it. And there is a second error in your idea that you don't see but I will hold back on saying it until you describe in better detail what you are thinking.

Edit: You could of course also make this circuit and see if the battery spontaneously charges.

 

[cianfa72]

See for instance Nyquist noise. Suppose the resistor's Thevenin model with a voltage source is connected through a diode to a cell battery. This way the cell battery stores chemical energy from thermal energy without limits.

 

[russ_watters]

See for instance Nyquist noise. Suppose the resistor's Thevenin model with a voltage source is connected through a diode to a cell battery. This way the cell battery store chemical energy from thermal energy without limits.

Draw and label a diagram, being very specific about what you think is happening (the numbers)

 

[cianfa72]

This is the diagram.

The diode D allows current to flow only in the cell recharging direction.

 

[Frabjous]

Sounds similar to a brownian ratchet.
https://www.feynmanlectures.caltech.edu/I_46.html
https://en.wikipedia.org/wiki/Brownian_ratchet

 

[russ_watters]

This is the diagram.
View attachment 343259
The diode D allows current to flow only in the cell recharging direction.

Add the numbers to it

 

[berkeman]

The diode D allows current to flow only in the cell recharging direction.

And what is the V-I characteristic of this diode at thermal noise voltages? (Hint: be sure to consider the reverse saturation current value...)

 

[cianfa72]

Sounds similar to a brownian ratchet.
https://www.feynmanlectures.caltech.edu/I_46.html
https://en.wikipedia.org/wiki/Brownian_ratchet

Very interesting. About Feynman analysis of the case where the two part are at same temperature $T$, I've a doubt.

He says the probability to get energy by a molecule hitting the paddle wheel from its heat bath reservoir to bring up the pawn is $e^{- \epsilon/kT}$. Similarly the probability that the pawl is accidentally up (by molecule hitting it from its heat bath reservoir) is again $e^{- \epsilon/kT}$.

The point I would make is that actually probabilities to turn the wheel forward and backward are not exactly the same (we can calculate them using the fact the events happening in the first and in the second reservoir are actually statistically independent).

 

[Bystander]

He says the probability to "absorb" energy by a molecule hitting the paddle wheel from its heat bath reservoir to bring up the pawn is e−ϵ/kT. Similarly the probability that the pawl is accidentally up (by molecule hitting it from its heat bath reservoir) is again e−ϵ/kT.

"Two statistically independent reservoirs?" Two? Think.

 

[phyzguy]

The Wikipedia article linked by @Frabjous even has the exact circuit you proposed, and explains why it doesn't work.

 

[cianfa72]

"Two statistically independent reservoirs?" Two? Think.

Why not ? In the experimental setup there are two boxes that act as two heat baths at the same temperature $T$. I believe we can safely assume that molecules and processes within them are actually statistically independent.

 

[cianfa72]

And what is the V-I characteristic of this diode at thermal noise voltages? (Hint: be sure to consider the reverse saturation current value...)

$$i= I_s(e^{v/V_T} - 1)$$ where $V_T \approx 26 mV$ at $T=300K$.

 

[PeroK]

TL;DR Summary: About the proposal of an experiment that at first glance violates the second law of thermodynamics

Hi, soppose we have a resistor at a given temperature T connected through a diode to a cell battery.

The voltage accross the resistor due to thermal noise should charge the cell converting termal energy into chemical energy without limits.

Does the above process violate the second law of thermodynamics ?

This must be one of the least inspiring attempts to violate the second law of thermodynamics. A battery, a resistor and a diode? Is that it?

Did you mean that it violates Ohm's law?

 

[berkeman]

$$i= I_s(e^{v/V_T} - 1)$$ where $V_T \approx 26 mV$ at $T=300K$.

Correct, and how much rectification action do you get for small AC voltages about zero Volts?

 

[cianfa72]

Correct, and how much rectification action do you get for small AC voltages about zero Volts?

Expanding the I/V curve by Taylor series around $v=0$ we get $$i \approx \frac {I_s} {V_T} v$$ i.e. the diode acts as a resistor of $V_T/I_s$ ohms for small AC voltages. Therefore there will not a net flux of energy recharging the cell battery

 

[lerus]

Can we say that it is not possible to create a perfect diode because otherwise it is possible to create device that violates 2 law of thermodynamics?

 

[cianfa72]

Can we say that it is not possible to create a perfect diode because otherwise it is possible to create device that violates 2 law of thermodynamics?

Yes, I believe it makes sense. We can claim it.

 

[lerus]

Yes, I believe it makes sense. We can claim it.

Thank you, are there other devices that are not allowed for the same reason?

 

[jbriggs444]

Thank you, are there other devices that are not allowed for the same reason?

For instance, Maxwell's Demon? Or a perfect ratchet? Or a lens arrangement that heats a real image hotter than the source?

 

[Vanadium 50]

You need to better define "perfect diode", but I strongly suspect your definition will have this diode at absolute zero temperature.

 

[lerus]

You need to better define "perfect diode", but I strongly suspect your definition will have this diode at absolute zero temperature.

Perfect diode is a device which electrical resistance is
$R = 0$ , when $V > 0$ and
$R=\infty$ when $V<0$

 

[lerus]

For instance, Maxwell's Demon? Or a perfect ratchet? Or a lens arrangement that heats a real image hotter than the source?

I agree, probably "semi mirror" that reflects all light that goes for instance from right to left but transparent for light that goes from left to right

 

[Vanadium 50]

Perfect diode is a device which electrical resistance

And how do you define resistance?

You are getting close to the idea that a perfect diode is at absolute zero.

 

[lerus]

I think resistance is a coefficient between current and voltage
$$V = I R$$
for extreme cases if $R=0$ it means that always $V=0$
and if $R=\infty$ it means that always $I=0$

 

[Philip Koeck]

I agree, probably "semi mirror" that reflects all light that goes for instance from right to left but transparent for light that goes from left to right

I would say this "semi mirror" doesn't even have to be perfect as you describe it.
Any "passive" mirror that transmits a bit more in one direction and reflects a bit more in the other should be in conflict with the 2nd law.

By "passive" I mean that it doesn't require energy input.

If you just imagine two large, plane surfaces at the same temperature and then you put such a mirror between them the one surface would heat up and the other would cool down.

Do you agree?

 

[jbriggs444]

I would say this "semi mirror" doesn't even have to be perfect as you describe it.
Any "passive" mirror that transmits a bit more in one direction and reflects a bit more in the other should be in conflict with the 2nd law.

By "passive" I mean that it doesn't require energy input.

If you just imagine two large, plane surfaces at the same temperature and then you put such a mirror between them the one surface would heat up and the other would cool down.

Do you agree?

If the semi-mirror were imperfect (absorbed some fraction of the radiation impinging on it) then the concern would arise about how it would re-emit that radiation. So now we have that complexity to contend with.

 

[Philip Koeck]

If the semi-mirror were imperfect (absorbed some fraction of the radiation impinging on it) then the concern would arise about how it would re-emit that radiation. So now we have that complexity to contend with.

I agree. That's why I only considered transmission and reflection. The semi-mirror shouldn't absorb.

 

[Vanadium 50]

If you require V to be identically zero, you require the thermal noise to be zero as well, i.e. T = 0.

If you have a resistor at T > 0 and a diode at T = 0, you have a heat engine. Of course you can extract work.

 

[lerus]

Thank you for your answer.
I agree, but just $V=0$ is not enough to extract work. It's a combination of $V=0$ and $I=0$ that extracts work.
Is it correct that ability to extract work from thermal noise contradicts to the second law of thermodynamics?

And one more question, sorry. Does superconductor produce thermal noise? If it doesn't then we have one half of prefect diode and $T>0$. Probably somebody else could figure out how to create the other half of perfect diode :).

 

[Vanadium 50]

Again, you are discussing a heat engine. You extract work by having part of it at one temperature and part at another. The fact that the components are electrical and not mechanical is irrelevant.

Imagining one part kept at absolute zero, even implicitly, gets you a Perpetual Motion Machine. We do not discuss these here, but armies of people have tried to make them, and have them "almost work - as soon as I get this last part right."