Find n from PV^n=C

[Gorz]

Homework Statement

Question is to rearange the formula PV^n=C to find n

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

 

[tiny-tim]

Welcome to PF!

Hi Gorz! Welcome to PF!

(try using the X² and X₂ tags just above the Reply box )

Question is to rearange the forumula PV^n=C to find n
…
Using logs i come up with n=(P2/P1).ln(V2/V1)

uhhh? whatever are P1 P2 V1 and V2? and where did C go?

 

[Gorz]

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

 

[tiny-tim]

perhaps i'm misunderstanding the question …

Question is to rearange the forumula PV^n=C to find n

… but the next step seems to be Vⁿ = P/C, so ln … ?

 

[Gorz]

perhaps i'm misunderstanding the question …


… but the next step seems to be Vⁿ = P/C, so ln … ?

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.

 

[Gorz]

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:

 

[Gorz]

I fear i might start losing some sleep over this.

 

[orthovector]

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:

remember you need to work with SI units. bars must be converted into pascals.
other than that, it looks okay to me so far. remember what you are doing. that relationship stems from the adiabatic process of an ideal gas where n = Cp/Cv.

 

[Gorz]

remember you need to work with SI units. bars must be converted into pascals.
other than that, it looks okay to me so far. remember what you are doing. that relationship stems from the adiabatic process of an ideal gas where n = Cp/Cv.

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:

 

[Redbelly98]

You're value of n is correct given the P1, P2, V1, and V2 you said earlier.

Were the pressures and volumes given, or did you derive/find them somehow?

Also you're correct, units don't matter since we are dealing with ratios.

Finally, why do you say 1<n<2? I know that's true for an adiabatic process in an ideal gas, is that the case here?

 

[Gorz]

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.