Homework Help: Find n from PV^n=C

1. The problem statement, all variables and given/known data
Question is to rearange the formula PV^n=C to find n


3. The attempt at a solution
Using logs i come up with n=(P2/P1).ln(V2/V1)

I understand that this is a really easy question, im just having a mind block from all the studying ive been doing lately.

Thanks

 

ok.

PVⁿ=C

Therefore P₁V₁ⁿ=P₂V₂ⁿ

Rearrange and you can get (P₁/P₂)=(V₂/V₁)ⁿ

Taking logs of this you get ln(P₁/P₂)=n.ln(V₂/V₁)

Not sure if im right thus for, so cant continue.

:(

P₁=3.38bar
P₂=1.2bar
V₁=0.03m²
V₂=0.2m²

 

C, the constant is P₂V₂ⁿ

So it needs to be rearranged so you have both sets of pressure and volume on each side as you are not given the constant as a value.

Whats annoying is I done this problem about 3 weeks ago, but ive not had it back from the university yet to look at my working. I know im nearly there, im just making a small mistake somewhere.

 

Correct me if im wrong.

log(P₁/P₂)=log(V₂/V₁).n

Giving n: [log(P₁/P₂)/log(V₂/V₁)]

Putting in values gives 0.546.

It should be 1<n<2

:uhh:

 

I fear i might start losing some sleep over this.

 

n is not = Cp/Cv in this case though, as that would yield the value for gamma, PV^gamma=C, which is already been used for a previous process earlier in the question.

This process is Polytropic.

Also on the note of converting to N/m2 (Pa), surely the ratio of P1/P2 will be exactly the same when I use bar in this instance.

I think the problem with my value for n may lie in my previous working to find the pressure at the start of this process. :uhh:

 

The value for P1 is derived, but I realised that a mistake in earlier working meant that was wrong.

It is a polytropic process, hence 1<n<2

Cheers for the help guys.