Entropy, resistor in a temperature bath

In summary, the process of adding heat to a resistor results in a decrease in entropy, but only for the portion of the cycle where heat is added.
  • #1
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 teh cycle have I made a mistake?
 
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  • #2
I expect it has something to do with the last step not being reversible.
 
  • #3
Sorry, put this in the wrong section, please feel free to move it.
 
  • #4
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
 
  • #5
Thanks Andrew, cleared it right up.
 

1. What is entropy?

Entropy is a measure of the disorder or randomness in a system. It is often referred to as "disorder" or "chaos", but in a scientific context, it represents the number of possible arrangements or states that a system can have.

2. How does entropy relate to a resistor in a temperature bath?

In the context of thermodynamics, entropy is closely related to a resistor in a temperature bath. The resistor represents a system that is constantly exchanging energy with its surroundings, just like a temperature bath. The flow of energy in and out of the system increases the disorder and therefore the entropy of the system.

3. Why is entropy important in thermodynamics?

Entropy is a fundamental concept in thermodynamics as it helps us understand how energy flows and changes in a system. It is used to explain processes such as heat transfer, chemical reactions, and phase changes. Entropy also plays a crucial role in the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time.

4. How is entropy measured?

The unit of measurement for entropy is joules per kelvin (J/K). This reflects the relationship between entropy and temperature, as a change in temperature can cause a change in the disorder of a system. However, entropy cannot be directly measured as it is a theoretical concept, so it is often calculated using other thermodynamic properties such as heat and temperature.

5. Can entropy be reversed?

The second law of thermodynamics states that the total entropy of a closed system will always increase, and it is nearly impossible to reverse this process. However, in some cases, the entropy of a specific system can be decreased, but this will always result in an overall increase in the entropy of the surrounding environment.

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