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# Joule-Thomson Expansion Effect - What's The Fundamental Relationsh

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### #1 6thSense

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Posted 09 July 2020 - 01:45 PM

I've been thinking in circles about the relationship between the key variables in relation to the JT Expansion Effect. I'm particularly talking about a situation where the expansion takes place across a valve. Please help clarify...

I've read almost every source but all that is defined is the Joule-Thomson coefficient which describes the dT/dP i.e., magnitude of cooling per magnitude of pressure drop. But from my understanding, the actual cooling fundamentally happens due to the expansion, particularly in the form of PV increase.

1. So shouldn't there be a straightforward relationship between the magnitude of expansion (specifically magnitude of PV increase) and the magnitude of cooling?

2. Very importantly related to the above question: What actually determines the magnitude of the PV increase?

3. Also, dT/dp is well known to increase as temperature decreases. Again, what is the effect of temperature on PV increases?

So I guess you can say, with the JT phenomenon, I'm trying to nail down the relationship between T, P and V specifically in terms of magnitude.

Thanks so much in advance! Any help is appreciated!

### #2 Bobby Strain

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Posted 09 July 2020 - 07:06 PM

You will need an equation of state for the fluid to get what you desire.

Bobby

### #3 6thSense

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Posted 09 July 2020 - 07:49 PM

You will need an equation of state for the fluid to get what you desire.

Bobby

Hi Bobby,

I do understand that you need an EOS to actually calculate the values and stuff.

But I'm not trying to seek out how to calculate the actual values even do mathematical derivations but rather I'd like to just understand conceptually the relationship between these variables qualitatively. In other words...

What I'm asking in Question #1 is this: We know that there's a fixed temperature drop for a given pressure drop (defined by Joule-Thomson coefficient) for a given temperature. Likewise, is there also a theoretically fixed relationship between temperature and volume so that there is a fixed temperature drop for a given magnitude of expansion? We don't have to come up with the exact actual expression for that relationship, but is there even such a relationship like there is between dT and dP? If so, does it also vary with temperature?

What I'm asking in Question #2 is this: Again I'm simply curious what determines the magnitude of this PV Increase (Expansion Work) conceptually? Does lower temperature mean bigger PV increase? Or is it determined by the volume before expansion? Or something else?

What I'm asking in Question #3 is this: This is extension of the previous question. Is there any effect of temperature on the actual PV increase? If so, which way does it effect it?

Hope my questions make more sense.

Thanks a lot for any help!

### #4 breizh

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Posted 09 July 2020 - 09:36 PM

Hi,

Consider the documents attached to support your work.

Hope this is helping you .

Breizh

### #5 MrShorty

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Posted 10 July 2020 - 11:56 AM

The key thing that I think is missing from your description of the Joule Thompson effect is that the expansion is isenthalpic -- that is, the change in enthalpy from initial to final state is 0. So my cautious answer to question 1 is H(P1,V1,T1)-H(P2,V2,T2)=0. Ignoring for now the complexities of calculating enthalpy from PVT, I would suggest that this is your "straightforward" relationship between state 1 and state 2.

I think there is a lot going on in question 2. Off the top of my head, most of my thoughts revolve around how it all depends on the exact nature of the specific fluid. Some fluids (like H2 and He at room temperature) warm rather than cool on expansion. In other cases (like most refrigerants) we set up the expansion so that state 1 corresponds to a liquid state and state 2 is a gas state so that the latent heat of vaporization contributes to the amount of cooling (and, of course, a very large PV expansion as the fluid changes phase).

I'm not quite sure what question 3 is asking, but I would return to the simple expression in 1 and say that whatever effect temperature has on the PV increase, it is constrained by the relation that the expansion is isenthalpic.

I wonder if it would be valuable to pull up a few Mollier diagrams (or similar diagram that will show you lines of constant enthalpy) to see what they will show you. You can pick a starting or an ending state and follow the line of constant enthalpy to see what other states can connect to that state via a JT expansion.