How much work is done by the Adiabatic Compression of Diatomic Gasses

1. Feb 16, 2016

grandpa2390

I apologize if my questions were in the wrong place. I am in "Advanced" Physics Classes. And so I post the questions from those classes in the Advanced Physics forum. And these are questions that weren't covered in Introductory Physics (1st three semesters). But they keep being moved to this forum. I don't understand the criteria. I guess that forum is for doctoral students and above? The "Really Advanced" stuff lol. regular graduate level classes and below go here? Want to make sure my questions are in the right place.

1 liter of ideal diatomic gas (allow for rotation but not vibration) at a pressure of 1 atmosphere and a temperature of 300 K is compressed adiabatically to a pressure of 7 atm. What is the volume of the gas after compression?

so I found the volume to be .249 Liters
the final temperature after compression is 523 K

what I can't find is the work that was done during compression on the gas.
I drew a graph of the compression and found the equation of the line to be $(-6/.751)$*v+8.989=p
i then tried integrating that over v from 1 Liter to .249 Liters. but the answer I got of 303 J is wrong...

What am I doing wrong?

I apologize about not having the guidelines on here. I accidentally erased them, and then the forum saved the draft. and I can't get them back...

2. Feb 17, 2016

Staff: Mentor

One thing from the homework template that is missing is the "Relevant equations" part. Can you write the relevant equations?

Also, it is very helpful for the helpers to see the details or your previous calculations.

3. Feb 17, 2016

ehild

What is the relation between pressure and volume during an adiabatic compression/expansion? It is not linear!

4. Feb 17, 2016

grandpa2390

You are right. In class he did an example that was not linear. I'm not sure what the relationship is though because in the example it wasn't necessary. We did get a formula using log(T/T2), maybe that one is it

ln(T2/T1)^3/2 = ln (v1/v2)...

or no, this one. W=-NKTln(V2/V1) is probably my best bet

no, that didn't work. I realized that formula is for isothermic because it only takes one T into account.

I found on another post where the helper asked if the person could find $C_v$ I found it using (f/2)NK but I don't understand the rest of his post to see how it is relevant. https://www.physicsforums.com/threads/work-required-for-adiabatic-compression.644227/

Last edited: Feb 17, 2016
5. Feb 17, 2016

Staff: Mentor

6. Feb 17, 2016

grandpa2390

7. Feb 17, 2016

ehild

What is the relation between P and V during an adiabatic expansion/compression?
You have to integrate pdV to get the work. Express P with V.

8. Feb 17, 2016

grandpa2390

they are inverses (as one rises, the other falls). And they are not linearly related...

I know I have to integrate. I di that initially. the problem is I don't know the relationship. I'm going to try V^gamma = 1/P

9. Feb 17, 2016

ehild

It is close, but not correct. What is the relation exactly between P and V?

10. Feb 17, 2016

grandpa2390

I don't know. I have looked through my notes 5 times, and that's all I have got. :(

he just said it was equal to a constant.

I have another formula he said was equal to a constant. VT^3/2

is VT^f/2 = PV^gamma?

11. Feb 17, 2016

ehild

12. Feb 17, 2016

grandpa2390

13. Feb 17, 2016

grandpa2390

14. Feb 17, 2016

vela

Staff Emeritus
This is the kind of problem you do in a freshman/sophomore physics class. The advanced physics forum is for upper division and beyond. A good indicator is if the answer you're looking for is a numerical one, it's probably an intro physics question.

You need to learn how to read the book. It's a skill like any other, and you have to develop and practice it. Don't expect to be able to simply read the book and have the material be clear to you on the first or second pass. If it were that easy, you wouldn't need to take a class.

15. Feb 17, 2016

grandpa2390

Exactly! That is why I am here.
I have read the chapter several times and the linked articles. If I say it went over my head, then I am not lacking the skill, I am lacking the background.

Last edited by a moderator: Feb 17, 2016
16. Feb 17, 2016

Staff: Mentor

You still haven't answered my question about the relevant equations. What equations to you have involving work?

17. Feb 17, 2016

grandpa2390

I did answer it. W= (integral of) -pdv
You take the equation of the line and find the area beneath it. Then multiply that by 101 and that gives you work. My problem is I don't know how to find the equation of the line for adiabatic compression/expansion. I emailed my professor though. @ehild did the best he could for me. It sounds like it is a very simple formula or algorithm that I am missing. If I weren't 9 credit hours from graduating, I'd switch majors... :(
once again, thanks for trying in a respectful manner.

18. Feb 17, 2016

grandpa2390

My professor explained to me what it is. W=-Pi*Vi^(7/5)*integral(Vi, Vf, V^(-7/5)*dV). I told you I was an idiot. Vi and Vf are constants. We know them. Vf is the variable. I was expecting, for some reason, a line that could be graphed without initial conditions. I'm an idiot. :)

it's not an inability to read. I proposed that solution earlier, but a dumb flaw in my reasoning prevented me from pursuing it.

19. Feb 17, 2016

ehild

Remember:

pVγ is constant along a reversible adiabat. (γ=Cp/Cv)

which means that P2V2γ=P1V1γ. You know P1, V1 and P2. It is diatomic gas, from that you get γ, and you can calculate V2.
From the equation for an adiabat, $P=P_1\frac{V_1^\gamma}{V^\gamma}$, so
$W=-\int_{V_1}^{V_2}{P_1\frac{V_1^\gamma}{V^\gamma}dV}$