Rate of entropy generation (can it be negative?)

In summary, the conversation discusses the Clausius inequality and the definition of entropy, which leads to the increase of entropy principle. It is stated that Sgen cannot be negative, but the rate of Sgen, \dot{S}_{gen}, can be negative. The conversation also mentions the relevance of rates of processes in thermodynamics and the importance of defining initial and final states. The concept of entropy generation is explained, using the example of a device with varying levels of friction. The conversation concludes by discussing the practical application of thermodynamics and the simplicity of understanding it.
  • #1
JJBladester
Gold Member
286
2

Homework Statement



The Clausius inequality combined with the defintion of entropy yields an inequality known as the increase of entropy principal, expressed as

Sgen ≥ 0

where Sgen is the entropy generated during a process.

Homework Equations



Sgen ≥ 0

The Attempt at a Solution



I know that Sgen cannot be negative, but can the rate of Sgen, [itex]\dot{S}_{gen}[/itex] be negative?
 
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  • #2
I do believe. You mean the entropy generates fast at first and slow later. Why not.
 
  • #3
dikmikkel said:
I do believe. You mean the entropy generates fast at first and slow later. Why not.

That was my thought but I wasn't sure as this whole entropy thing is rather new to me.

I reasoned that if a car going 50mph slows down to 40mph, it still has a positive velocity, but the velocity derivative (acceleration) is negative. Likewise, Sgen's time rate of change can be negative although entropy generated overall can only be positive. Test on Friday... I hope I'm right!
 
  • #4
Thermodynamics (Equilibrium) neither entertains (asks) nor answers questions concerning the rates of processes. Rates of processes is irrelevant to find answers to questions in thermodynamics. Once the initial and final states of a system are defined, the process connecting them could be of any rate (could be infinitely fast/slow), the result of the entropy change will be the same.
It would perhaps be better to write the equation as delta S universe greater than or equal to zero instead of Sgen greater than or equal to zero, to reduce possible ambiguity and misinterpretations.
 
  • #5
Radhakrishnam said:
Thermodynamics (Equilibrium) neither entertains (asks) nor answers questions concerning the rates of processes. Rates of processes is irrelevant to find answers to questions in thermodynamics. Once the initial and final states of a system are defined, the process connecting them could be of any rate (could be infinitely fast/slow), the result of the entropy change will be the same.
It would perhaps be better to write the equation as delta S universe greater than or equal to zero instead of Sgen greater than or equal to zero, to reduce possible ambiguity and misinterpretations.

I think what Radhakrishnam is alluding to here is that the constrained form of the Clausius inequality described by you in the OP applies to a closed, adiabatic system (i.e., an isolated system). The entire universe can be regarded as a closed, adiabatic system. The more general form of the Clausius inequality, applicable to closed (but not necessarily adiabatic) systems is dS > dq/T.
 
  • #6
Radhakrishnam said:
Thermodynamics (Equilibrium) neither entertains (asks) nor answers questions concerning the rates of processes. Rates of processes is irrelevant to find answers to questions in thermodynamics.

That is true. Fair enough. But aside from that, I want to know what happens along the way, not just at the endpoints. If it's not under the umbrella of thermodynamics, in what area of science may my question be asked?

Chestermiller said:
I think what Radhakrishnam is alluding to here is that the constrained form of the Clausius inequality described by you in the OP applies to a closed, adiabatic system (i.e., an isolated system). The entire universe can be regarded as a closed, adiabatic system. The more general form of the Clausius inequality, applicable to closed (but not necessarily adiabatic) systems is dS > dq/T.

Entropy Generation Definition:
Entropy generated (Sgen) during a process is a measure of the irreversibilities of that process.

Lets say you have a device that is rougher in one area than another and when the parts move in the device, more friction occurs as the parts make contact with the rough area.

The rate of entropy generation would be positive through this rough patch because the device introduces more irreversibility (friction) here. Then as your parts go back to moving smoothly and they are not touching the rough area, the friction subsides and the rate of entropy generation would be negative.

Does this make sense? This would make it sound like the rate of entropy generation could be negative.
 
  • #7
JJBladester said:
That is true. Fair enough. But aside from that, I want to know what happens along the way, not just at the endpoints. If it's not under the umbrella of thermodynamics, in what area of science may my question be asked?

Since we can choose the initial and final states as we please, it is possible to get the information at every point of the path (remember, it must be a reversible path). Along non-reversible paths the system will not be in a state of equilibrium and the properties of the system accordingly will be ill-defined.

Since your question concerns entropy, if and when you understand entropy well, you will find your question does not hold good - the question would disappear.



Entropy Generation Definition:
Entropy generated (Sgen) during a process is a measure of the irreversibilities of that process.

Lets say you have a device that is rougher in one area than another and when the parts move in the device, more friction occurs as the parts make contact with the rough area.

The rate of entropy generation would be positive through this rough patch because the device introduces more irreversibility (friction) here. Then as your parts go back to moving smoothly and they are not touching the rough area, the friction subsides and the rate of entropy generation would be negative.

Does this make sense? This would make it sound like the rate of entropy generation could be negative.

Thermodynamics gives whether a given process under given conditions is possible or impossible, in principle. when a process is known to be possible, the rate at which it is possible to carry out that process in practice depends upon the kinetics which takes into account the presence of catalysts, for example, etc. But that would not help in finding out the rate of generation of entropy.

Thermodynamics is much simpler to understand and appreciate than what it is projected to be in many books.
 
  • #8
JJBladester said:
That is true. Fair enough. But aside from that, I want to know what happens along the way, not just at the endpoints. If it's not under the umbrella of thermodynamics, in what area of science may my question be asked?



Entropy Generation Definition:
Entropy generated (Sgen) during a process is a measure of the irreversibilities of that process.

Lets say you have a device that is rougher in one area than another and when the parts move in the device, more friction occurs as the parts make contact with the rough area.

The rate of entropy generation would be positive through this rough patch because the device introduces more irreversibility (friction) here. Then as your parts go back to moving smoothly and they are not touching the rough area, the friction subsides and the rate of entropy generation would be negative.

Does this make sense? This would make it sound like the rate of entropy generation could be negative.

Here are some suggestions on how to begin to get a handle on what you are looking for:

1. Bird, Steward, and Lightfoot "Transport Phenomena" has a homework problem that looks at entropy generation in non-equilibrium continua.

2. Look up non-equilibrium thermodynamics in Wikipedia

3. Get a book on Statistical Thermodynamics, and get an idea how entropy is expressed in terms of the total number of quantum mechanical states available. Then start looking at how the molecular dynamics guys use statistical thermo to quantify entropy (and other thermodynamic entities) in systems that are not at equilibrium.
 

1. What is the rate of entropy generation?

The rate of entropy generation is a measure of the amount of disorder or randomness that is being created in a system. It is a thermodynamic property that describes the rate at which energy is being dissipated or lost in a system.

2. How is the rate of entropy generation calculated?

The rate of entropy generation is calculated using the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time. It can be calculated by dividing the heat transfer into a system by the temperature at which the heat is transferred.

3. Can the rate of entropy generation be negative?

No, the rate of entropy generation cannot be negative. This is because the second law of thermodynamics states that entropy always increases and never decreases. A negative rate of entropy generation would imply that entropy is decreasing, which is not possible according to this law.

4. What factors affect the rate of entropy generation?

The rate of entropy generation is affected by several factors, including the temperature difference between the system and its surroundings, the efficiency of energy conversion processes, and the complexity of the system. Higher temperature differences and lower efficiency will result in a higher rate of entropy generation.

5. How does the rate of entropy generation relate to energy efficiency?

The rate of entropy generation is directly related to energy efficiency. The higher the rate of entropy generation, the lower the energy efficiency of a system. This is because a higher rate of entropy generation means that more energy is being lost or dissipated in the form of heat, reducing the overall efficiency of the system.

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