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