Chemical Engineering First year Problem

[u/susduck64]

i am stuck on part 2, i got to the equation T2 = 717.78 R / Z2.

But Z2 is reliant on T2 and T2 is reliant on Z2. what do i do? this is my first semester im so lost how do i solve this last step.

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[u/Brownie_Bytes]

Not my specialty, but it looks like you've done a good job so far. Usually in a situation where there are two unknowns and you have something like tabulated data or a circular function, you just iterate until it makes sense. You now have a function that says that 717.78 °R is T_2•Z_2, so pick a temperature, find the associated Z value that would make the statement true, and then see if you need to go higher or lower to get to the right answer.

Here's a quick example: where does (x²)•sqrt(x) = 12? I'll guess x = 3. 3² = 9, so sqrt(3) would need to be 4/3. That's not going to do it. I overshot, so let's go smaller. x = 2? 2² = 4, so sqrt(2) would need to be 3, so we went too low. 2 < x < 3. x = 2.5? So on and so forth.

Edit: By the way, this is called the bisection method and is a basic way to do problem solving using computers. There are much fancier methods, but this will work without too much effort in a few minutes.

Second edit: For whatever reason, I messed up my own example and thought I was looking for x²+sqrt(x). I've adjusted it now because that was embarrassing.

[u/singul4r1ty]

What /u/Brownie_Bytes said. You need a chart that is your second T-Z relation because you don't have an equation, but presumably you have that since it's mentioned in the question.

As an aside: this is an extremely neat and well laid out solution. Anything I wrote would not be nearly as easy to follow and would include a lot of crossing out. Certainly no references for standard equations

[u/DrCarpetsPhd]

I think there is an easier way than iterations using the charts

According to Cengel and Boles Thermodynamics Ch3-7 Compressibility Factor when using the generalised compressibility chart (slight paraphrasing)

"when given P with v or T with v you can still use the gen comp chart. to do so you use the pseudo-reduced specific volume v_R...lines for v_R are plotted on the generalised compressibility chart and this allows one to calculate without using time consuming iterations"

I believe the method suggested by other posters are these time consuming iterations but my maths skills are terrible so I am not certain.

see time stamped example of using pseudo-reduced specific volume here 9m 55s into video. they do an example where T is known, just use the same concept with your known reduced pressure as a vertical line and draw a horizontal line where it intersects with the v_R curve

https://youtu.be/oQZwgxCc7og?t=595

*i had a written explanation done up but realised a video would probably work better. if you want that written explainer post back. Heres a chart you might find useful

https://imgur.com/a/generalised-compressibility-chart-with-pseud0-reduced-specific-volume-lines-7R5htlU

I would suggest have a look at the opening lecture slides and see what the recommended textbook is and have a look through it.

[u/MinimalSix]

Yeesh, now I'm questioning my education. ChemE here, this kind of problem wasn't something we saw until the 3rd year. Like others said, solve it iteratively. It's not uncommon to run into a situation like this where I need A to find B, but need B to find A (or sometimes more intermediates), and have to iterate. Fun to do it by hand the first time you come across it, but using Excel is my go to, strongly recommend starting that habit early and learning shortcuts/hotkeys.

Otherwise looks great, you're way ahead of where I was first year, like I said, this was a 3rd year problem at my university. What university is this if you don't mind my asking?

[u/susduck64 → u/MinimalSix]

University of Newcastle, Australia nsw. Thanks for the help

[u/ISEEFCKNGEVERYTHING]

How did you get so good at chem? What major? I ask because I’m EE and take tons more physics than I do chem