Entropy, resistor in a temperature bath

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Discussion Overview

The discussion revolves around the change in entropy of a resistor in a constant temperature bath while current flows through it. Participants explore the thermodynamic implications of work and heat transfer in this context, aiming to understand the conditions under which the change in entropy can be considered zero.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asserts that the change in entropy of the resistor is zero due to no change in its thermodynamic state, seeking a reversible process to demonstrate this.
  • Another participant suggests that the last step of the process may not be reversible, indicating a potential flaw in the reasoning.
  • A different perspective emphasizes that the heat flow into the resistor from electrical energy must be considered, equating it to heat flow from a reservoir, which could affect the entropy calculation.
  • It is noted that the heat flow into and out of the resistor occurs at the same temperature, suggesting no change in entropy for the resistor.

Areas of Agreement / Disagreement

Participants express differing views on the conditions under which the change in entropy can be considered zero, with some arguing for the validity of the initial claim and others challenging the assumptions made in the calculations. The discussion remains unresolved regarding the correct interpretation of the entropy change.

Contextual Notes

Limitations include the dependence on the definitions of reversible processes and the assumptions made about heat flow and thermodynamic states. The mathematical steps leading to the entropy calculations are not fully resolved.

nnnm4
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Consider a resistor with current running through it for some time in a constant temperature bath. I understand that the change in entropy of the resistor is zero because there is no change between the initial and final thermodynamic state. However, I am trying to come up with a reversible process in which to calculate explicitly the change in entropy as zero.

First I initially consider the work performed on the resistor and no heat is added.

TdS = dU - dW = 0, since the change in the energy is due solely to the work.

Then the resistor is brought into contact with the bath and heat flows from the resistor to the bath

TdS = -dW = -I^2*R*t.

So I'd get a negative change in entropy for the entire process (for the resistor). Where in the cycle have I made a mistake?
 
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I expect it has something to do with the last step not being reversible.
 
Sorry, put this in the wrong section, please feel free to move it.
 
nnnm4 said:
Consider a resistor with current running through it for some time in a constant temperature bath. I understand that the change in entropy of the resistor is zero because there is no change between the initial and final thermodynamic state. However, I am trying to come up with a reversible process in which to calculate explicitly the change in entropy as zero.

First I initially consider the work performed on the resistor and no heat is added.
Heat is added. If you stopped the heat flow out of the resistor, the temperature of the resistor (and, hence, its internal energy) would keep increasing.

TdS = dU - dW = 0, since the change in the energy is due solely to the work.

Then the resistor is brought into contact with the bath and heat flows from the resistor to the bath

TdS = -dW = -I^2*R*t.

So I'd get a negative change in entropy for the entire process (for the resistor). Where in the cycle have I made a mistake?
You are not taking into account the heat flow into the resistor in the form of electrical energy. Electricity is converted into heat in the resistor. This is thermodynamically equivalent to heat flow into the resistor from a heat reservoir.

The heat flow into the resistor is the same as the heat flow out of the resistor and they both occur at the same temperature, so there is no change in entropy of the resistor.

AM
 
Thanks Andrew, cleared it right up.
 

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