Calculating Entropy of Systems

[rwooduk]

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.

 

[Andy Resnick]

<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.

 

[Chestermiller]

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.

 

[rwooduk]

Many thanks for the replies.

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".

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.

 

[Chestermiller]

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.

 

[rwooduk]

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

 

[Chestermiller]

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.

 

[Andy Resnick]

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

It's an integral expression derived using the Reynolds transport theorem:

http://se.asee.org/proceedings/ASEE2013/Papers2013/138.PDF

 

[rwooduk]

It's all in Bird et al.

It's an integral expression derived using the Reynolds transport theorem:

http://se.asee.org/proceedings/ASEE2013/Papers2013/138.PDF

Excellent. I will give it a try, thanks again for your help!