# Polytropic Process Index -- help please

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1. Feb 21, 2016

1. The problem statement, all variables and given/known data
"Determine the polytropic process index 'n' from the initial and final condition parameters of the air (gas) in the air compressor cylinder."

Im struggling with this question on my thermodynamics coursework and was wondering if anyone could help me out a little bit.

2. Relevant equations
Im using the equation p1V1^n = p2V2^n and the values im given are:

p1 = 1.6 bar
V1 = 0.04m^3
p2 = 11425608.39 Pa
V2 = 0.0015m^3

It also says the law of the process is pV^1.3 = C

3. The attempt at a solution
The answer im getting is n = 1.3 but my tutor says its wrong and im not sure where im going wrong as im using the same equation as i used for my mock assessments and its basically the same question just with different values and my mock was an expansion where this is a compression.

Any help would be greatly appreciated.

Thanks

2. Feb 21, 2016

### Staff: Mentor

Are you working in terms of natural logs?

3. Feb 22, 2016

### Staff: Mentor

What units of pressure are you using here?

4. Feb 22, 2016

### Staff: Mentor

The units don't matter because the equation is dimensionless.

5. Feb 22, 2016

### Staff: Mentor

$$\ln{P}+n\ln{V}=\ln{C}$$So
$$n=-\frac{\Delta (\ln{P})}{\Delta (\ln{V})}$$

6. Feb 22, 2016

### Staff: Mentor

It does matter if poster mixes the units as given.

Last edited by a moderator: Apr 18, 2017
7. Feb 22, 2016

### Staff: Mentor

Very true.

Last edited by a moderator: Apr 18, 2017
8. Feb 22, 2016

P1V1^n = P2V2^n
1.6 x 10^5 x 0.04^n = 11425608.39 x 0.0015^n
0.04^n/0.0015^n = 11425608.39/(1.6 x 10^5)
26.67^n = 71.41
log 26.67^n = log 71.41
n log 26.67 = log 71.41
n = log 71.41/log 26.67
n = 1.3

Thats the working as i worded it on my assignment.

I also spent a good 3 hours going over example questions online yesterday regarding polytropic process and was correct on them all so its just this question that is throwing me out. My tutor says the answer im looking for is "just above 3 and abit".

Thanks for the responses.

9. Feb 22, 2016

### Staff: Mentor

I haven't verified your maths. I've gone back to your opening post.
Have I understood this correctly: your textbook gives you the problem, but also provides the answer? Their answer is 1.3, and your answer is also 1.3. But your tutor says you and the textbook are both wrong because your tutor's answer is close to 3?

10. Feb 22, 2016

### Staff: Mentor

I get n = 1.3. If your tutor says n = 3, you need to get a new tutor.

11. Feb 22, 2016

This is the question im given, Ive got answers for part a its just part b im struggling with.

"A compressor used in tyre fitting workshop is used to inflate commercial vehicle tyres to a high psi. The cylinder piston reciprocates and draws air in through an inlet valve and out via a discharge vale at a high pressure. During the cycle a quantity of air is compressed polytropically in the closed valve position. The law of the process being pV^1.3 = constant.

At the beginning of the process, the air has a volume of 0.04m^3 , a pressure of 1.6 bar and a temperature of 12oC.

a) At the end of the process, the volume of air is 0.0015m^3. Treating the air as a perfect gas, and as a reversible process calculate for the air in the cylinder:

(i) the mass

(ii) the final pressure before he discharge valve opens

(iii) the final temperature

For air, R =287 J/kgK

b) Determine the polytropic process index 'n' from the initial and final condition parameters of the air (gas) in the air compressor cylinder."

12. Feb 22, 2016

If you're still getting 1.3 from that information maybe i need to ask for a second tutors opinion as this question is stopping me getting distinction which is what I need.

Cheers guys

13. Feb 22, 2016

My tutors response to my query was:

"Okay some tips!

Its all down to the maths answer is over 3 and a bit

iTs a merit question from memory thats why its harder than the others

Have a valiant go!"

14. Feb 22, 2016

### Staff: Mentor

The guy gives you a problem in which $PV^n=C$ for the process, where n = 1.3, and then asks you to determine from the results of the calculation what the value of n is. And, somehow he expects it to come out something different from 1.3. What planet is he from? Then he reveals that he posed the problem based on his (possibly faulty) memory. He ought to be ashamed of himself for wasting your valuable time.

15. Feb 22, 2016

So what would you suggest I should do?

16. Feb 22, 2016

### Staff: Mentor

Refer him to us and see if he is up to the challenge.

17. Feb 22, 2016

my tutor also sent me this message regarding question one a while ago:

"Hi Andy

Task 1 the formulas to use are

P2/P1 = (V1/V2)^n

n=1.3"

So hes basically said himself that n = 1.3

18. Feb 22, 2016

### Staff: Mentor

Another option is to ask him to present his solution on Physics Forums.

19. Feb 22, 2016

### Staff: Mentor

I looked for the expected range of n. http://www.engineeringtoolbox.com/compression-expansion-gases-d_605.html says
If this is true, then a value of around 3 would seem way off, anyway.

20. Feb 22, 2016

### Staff: Mentor

This problem statement you then quote doesn't give a value for P2, you are required to calculate it using n=1.3. WHEREAS in your opening post, you seemed to be saying the problem statement provides both P1 and P2 and from these you are required to deduce n.

It does seem that part (b) is redundant, as you must inevitably arrive at n=1.3 since that's the value you're using.

How many moles did you calculate? Perhaps your tutor was referring to n, the number of moles of molecules?