Joule Thompson

I have been working on a series of questions dealing with gas expansion and temperature change for my PE exam.

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sorry having trouble with the latex thing so im just going to type it out,

dT/dP = 1/mCp(2a/RT - b) when I take the Bernoulli differential equation of this I get the following:

T2= (C1/C2 + c/exp(2*C2*P2))^.5 Where C1 = 2*a/m*Cp*R and C2 = b/m*Cp

where c is solved for using the intital conditions of T1 and P1

This equation is dependant upon mass, but also I am getting the temperature going in the wrong direction, this is very frustrating because I am trying to come up with a rigourus way of solving for T2 without using the fishy method they use in the PE solution manual where they iterate and practically guess a mass loss/gain in or out of the bottle.

 

I am kinda working the thermal expansion of methanol in tandum with joule thompson expansion. I am studying for my PE right now (along with doing that thermal expansion of methanol at work) and I am having the same set of problems dealing with air, I attempted to use joule thompson to model rapid expansion of gas (the calcs under methanol expansion actually apply more to joule thompson rather than liquid expansion). If you view the work I did attached to thermal expansion of methanol (and I will also attach the mathcad and updated hand calcs) you will see that you get temperature trends opposite of what is expected and after going through the first law derivation and a bernoulli differential equation its pretty frustrating because it should be correct for the rapid expansion of a gas, I was doing this in order to develop an equation for T2 in terms of pressure change using a vander walls equation of state.

All that being said I need to progress with my PE study so I have just been using the air tables at the back of the PE book but I am not sure what Vr actually is. In an otto cycle in the constant volume expansion V is constant from D to A but Vr is not what exactly is Vr, we never used air tables in college and while I can crank out the PE problems using the methods in the book I would really like to know what it is im doing.

This has been a very good site and I am glad I found it, it keeps me doing things that are useful and more away from political sites which just waste your time.

I have the updated joule thompson calcs worked out using the bernoulli differential equation (the roots of the methodology of solving first order non seperable differential equations will have to wait another day in a different section, but what is up with the integrating factor and why can you assume the constant of integration goes away, among other questions) and I will post them as soon as I can consolidate my work and scan everything in.

 

It is the chemical engineering PE exam book by professional publications. I have attached my final calcs, it would not allow me to attach xmcd files but this should be enough. The A was put there by another engineer that was looking at it at my desk while I was away from my desk and he was waiting to go to lunch with me, this was just for the first sheet deriving the joule thompson relationship.

 

Maybe I am taking an entirely wrong approch to this, maybe I should just be using an equation of state in its original format. However that being said, what would be the purpose of a joule thompson coefficent if you were just using an equation of state to solve for final temperature anyways. I know Hysys will calculate temperature drop through a valve using equations of state because I changed the equations of state and the outlet temperature changed.

I would greatly appriciate any help.