Calculating Entropy of Systems

In summary, according to the source, entropy is a measure of the disorder in a system. It can be generated by viscous dissipation (resulting from finite velocity gradients), heat conduction (resulting from finite temperature gradients), diffusive mass transfer (resulting from finite concentration gradients), and spontaneous chemical reaction (resulting from non-equilibrium chemical potentials).
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rwooduk
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This may not make sense but I'm going to throw it out there in hope of some suggestions.

If I have a system, for simplicity say particles in water and they are subject to a flow of some kind, as the flow is increased it becomes more turbulent and the particles are flying around all over the place, the entropy of the system has increased.

If I wanted to somehow quantify this in terms of entropy (disorder) then what factors would I need to consider, is there an equation that I could use and how would the parameters be introduced.

I always struggled with the concept of entropy at undergraduate level so my understanding is probably quite skewed, but I'm trying to understand it a little further from an experimental point of view, if that's possible?

Thanks for any help.
 
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rwooduk said:
<snip>If I wanted to somehow quantify this in terms of entropy (disorder) then what factors would I need to consider, is there an equation that I could use and how would the parameters be introduced.
<snip>

Interesting. Aside from using the usual energy equation, I have a reference that considers the pressure loss Δp as an entropy coefficient dC: Δp=ρ/2g ∫V2dC

(Hall, 'Thermodynamics of fluid flow'), but this is only for incompressible fluids.
 
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rwooduk said:
This may not make sense but I'm going to throw it out there in hope of some suggestions.

If I have a system, for simplicity say particles in water and they are subject to a flow of some kind, as the flow is increased it becomes more turbulent and the particles are flying around all over the place, the entropy of the system has increased.

If I wanted to somehow quantify this in terms of entropy (disorder) then what factors would I need to consider, is there an equation that I could use and how would the parameters be introduced.

I always struggled with the concept of entropy at undergraduate level so my understanding is probably quite skewed, but I'm trying to understand it a little further from an experimental point of view, if that's possible?

Thanks for any help.
Would you be willing to accept an explanation using Classical Thermodynamics in which viscous dissipation of mechanical energy is considered in a continuum approach, or does it have to be from the standpoint of statistical thermodynamics.
 
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Many thanks for the replies.

Andy Resnick said:
Interesting. Aside from using the usual energy equation, I have a reference that considers the pressure loss Δp as an entropy coefficient dC: Δp=ρ/2g ∫V2dC

(Hall, 'Thermodynamics of fluid flow'), but this is only for incompressible fluids.

I like this idea of relating pressure loss to entropy, in the system of the OP what, or should I say where would the pressure loss be applied or measurable? i.e. physically where would it be seen?

Also, please could you confirm the "usual energy equation".

Chestermiller said:
Would you be willing to accept an explanation using Classical Thermodynamics in which viscous dissipation of mechanical energy is considered in a continuum approach, or does it have to be from the standpoint of statistical thermodynamics.

I'm attempting to stay away from a statistical approach, dissipation of mechanical energy would more aptly fit my system, so any suggestion would be more than welcome.

I'm hesitant to make things more complicated, which is why I gave the particles in fluid example just to give me an idea of how parameters (and which parameters) should be introduced into an entropy interpretation, however, I'll add it anyway, the system I'm analysing is a cavitational system i.e. a transducer in contact with water which produces bubbles. There are lots of variables involved, heat, bubble-bubble interaction, frequency effects etc etc I'm trying to see if this system could be described using entropy as a measure of its disorder.

Thanks again, and I'd welcome any further input.
 
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The sources of entropy generation in a system are viscous dissipation (as a result of finite velocity gradients), heat conduction (as a result of finite temperature gradients), diffusive mass transfer (as a result of finite concentration gradients), and spontaneous chemical reaction (as a result of non-equilibrium chemical potentials). You can find a very interesting detailed analysis of this in Transport Phenomena by Bird et al, in Chapter 11, problem 11.D.1. A differential entropy balance is presented at the bottom of the table on page 341.
 
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Chestermiller said:
The sources of entropy generation in a system are viscous dissipation (as a result of finite velocity gradients), heat conduction (as a result of finite temperature gradients), diffusive mass transfer (as a result of finite concentration gradients), and spontaneous chemical reaction (as a result of non-equilibrium chemical potentials). You can find a very interesting detailed analysis of this in Transport Phenomena by Bird et al, in Chapter 11, problem 11.D.1. A differential entropy balance is presented at the bottom of the table on page 341.

Many thanks I will take a look. May I ask if any formulae are given? Would I have to create my own equation with each variable present in the experiment to give some sort of quantative value for the change in entropy?

Also for these "viscous dissipation, heat conduction, diffusive mass transfer and spontaneous chemical reaction" things might you suggest how they may appear physically i.e. finite velocity gradients of what?

Thanks again
 
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rwooduk said:
Many thanks I will take a look. May I ask if any formulae are given? Would I have to create my own equation with each variable present in the experiment to give some sort of quantative value for the change in entropy?

Also for these "viscous dissipation, heat conduction, diffusive mass transfer and spontaneous chemical reaction" things might you suggest how they may appear physically i.e. finite velocity gradients of what?

Thanks again
It's all in Bird et al.
 
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FAQ: Calculating Entropy of Systems

1. What is entropy and why is it important in systems?

Entropy is a measure of the disorder or randomness in a system. It is important in systems because it helps us understand the direction and efficiency of processes, and can also be used to predict the behavior of a system.

2. How is entropy calculated?

The formula for calculating entropy is S = k ln W, where S is the entropy, k is the Boltzmann constant, and W is the number of microstates in a system. The number of microstates can be determined by considering the possible arrangements of particles or energy states within a system.

3. Can the entropy of a system be negative?

No, the entropy of a closed system cannot be negative. This is because entropy is a measure of disorder, and a negative value would imply a negative amount of disorder, which is not physically possible.

4. How does entropy change in a reversible process?

In a reversible process, the entropy of the system remains constant. This is because the system is able to return to its original state, meaning there is no net change in disorder or randomness.

5. What factors affect the entropy of a system?

The factors that affect the entropy of a system include temperature, pressure, and the number of particles or energy states. Generally, an increase in temperature or pressure leads to a higher entropy, while a decrease leads to a lower entropy.

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