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# Polytropic Process Index 'n' help please watch

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1. Im stuck on a question on my coursework regarding finding the polytropic index 'n' and was wondering if anyone can help me out.

The question is:

"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 pV1.3 = constant.

At the beginning of the process, the air has a volume of 0.04m3 , a pressure of 1.6 bar and a temperature of 12oC.

At the end of the process, the volume of air is 0.0015m3.Treating the air as a perfect gas, and as a reversible process calculate for the air in the cylinder:

a)
(i) the mass
(ii) the final pressure before the 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"

I have answers for part a which have been marked as correct, but on part b) im getting an answer of n = 1.3, which is being marked as incorrect and im not sure where im going wrong. my tutor says the answer is nearer to "3.something"

Any help would be seriously appreciated as this question is knocking me down from a distinction to a pass, and obvioulsy id rather get a D.

Thanks
2. (Original post by jebbadiah)
Im stuck on a question on my coursework regarding finding the polytropic index 'n' and was wondering if anyone can help me out.

The question is:

"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 pV1.3 = constant.

At the beginning of the process, the air has a volume of 0.04m3 , a pressure of 1.6 bar and a temperature of 12oC.

At the end of the process, the volume of air is 0.0015m3.Treating the air as a perfect gas, and as a reversible process calculate for the air in the cylinder:

a)
(i) the mass
(ii) the final pressure before the 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"

I have answers for part a which have been marked as correct, but on part b) im getting an answer of n = 1.3, which is being marked as incorrect and im not sure where im going wrong. my tutor says the answer is nearer to "3.something"

Any help would be seriously appreciated as this question is knocking me down from a distinction to a pass, and obvioulsy id rather get a D.

Thanks
Post your working and we'll see where we can help.
3. 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.

Cheers

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