How Do You Calculate the Polytropic Process Index 'n' in Thermodynamics?

[Jebbadiah]

Homework Statement

"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.

Homework Equations

Im using the equation p1V1^n = p2V2^n and the values I am 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

The Attempt at a Solution

The answer I am getting is n = 1.3 but my tutor says its wrong and I am not sure where I am going wrong as I am 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

 

[Chestermiller]

Are you working in terms of natural logs?

 

[NascentOxygen]

p1V1^n = p2V2^n

What units of pressure are you using here?

Show your working.

 

[Chestermiller]

What units of pressure are you using here?

Show your working.

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

 

[Chestermiller]

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

 

[NascentOxygen]

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

It does matter if poster mixes the units as given.

 

[Chestermiller]

It does matter if poster mixes the units as given.

Very true.

 

[Jebbadiah]

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 I am looking for is "just above 3 and abit".

Thanks for the responses.

 

[NascentOxygen]

I haven't verified your maths. I've gone back to your opening post.

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

The Attempt at a Solution

The answer I am getting is n = 1.3 but my tutor says its wrong

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?

 

[Chestermiller]

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

 

[Jebbadiah]

This is the question I am given, I've got answers for part a its just part b I am 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."

 

[Jebbadiah]

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

 

[Jebbadiah]

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?

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 that's why its harder than the others

Have a valiant go!"

 

[Chestermiller]

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.

 

[Jebbadiah]

So what would you suggest I should do?

 

[Chestermiller]

So what would you suggest I should do?

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

 

[Jebbadiah]

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 he's basically said himself that n = 1.3

 

[Chestermiller]

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 he's basically said himself that n = 1.3

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

 

[NascentOxygen]

So what would you suggest I should do?

I looked for the expected range of n. http://www.engineeringtoolbox.com/compression-expansion-gases-d_605.html says

The polytropic process can be expressed as

pVⁿ = constant (3a)

or

p1V1ⁿ = p2V2ⁿ (3b)

where

n = polytropic index or exponent (ranging 1 to 1.4)

If this is true, then a value of around 3 would seem way off, anyway.

 

[NascentOxygen]

This is the question I am given

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?

 

[Jebbadiah]

I had to to find p2 in part a of the question using the equation P2/P1 = (V1/V2)^n, where i was told by my tutor that n = 1.3. I got an answer for p2 as 11425608.39 Pa, which my tutor has marked as correct. Then in part b "Determine the polytropic process index 'n' from the initial and final condition parameters of the air (gas) in the air compressor cylinder." I am using P1V1^n = P2V2^n to find n and getting n = 1.3, which is what he has already told me. but for some reason he is saying its incorrect. so surely if my answer of 1.3 was incorrect then that would also mean that my answer for p2 is incorrect as I've used 1.3 for my value of n. Hence why I am super confused by it.

 

[Znadeem]

please post the answer for part (a)