Thermodynamics- pV^n = constant.

[NBAJam100]

Homework Statement

A closed system consisting of 2 lb of a gas undergoes a process in which pV^n=constant. For: p1=20 lb/in^2 , V1=10 ft^3 and p2=100lb/in^2 V2=2.9 ft^3.

Find n.

Homework Equations

pV^n=constant

The Attempt at a Solution

Im just having trouble realizing how to find n. This seems very basic and maybe I am just rusty from having the summer off, this is a review question.

(p1)(V1)^n = (p2)(V2)^n

Now I am having trouble realizing how to re-arrange that to find n... I've tried using the relation p1V1^n=5P1(.29V1)^n but everything keeps canceling out. Can someone push me in the right direction?

Ive also tried solving for n in terms of C and plugging that back in and that just gives me a jumbled mess.

 

[Mapes]

The logarithm function turns exponential factors into multiplicative factors...

 

[NBAJam100]

The logarithm function turns exponential factors into multiplicative factors...

Yah I understand that. But Even if I do that won't I be left with:

n*ln(P1V1)=n*ln(P2V2)

So... All I can do is cancel things out. I can't really isolate n... right? unless I want #n=0.

Feel free to call me a moron if I am missing something obvious

 

[Mapes]

You're not taking the logarithm correctly.

 

[NBAJam100]

You're not taking the logarithm correctly.

Oh God I suck...

So does this sound good to you?

ln(P1(V1)^n)=ln(P2(V2)^n)

ln(P1) + n*ln(V1) = ln(P2) + n*ln(V2)

 

[Mapes]

Better!

 

[NBAJam100]

Better!

Awesome, thanks Mapes! How did I not see that

I got to say, I appreciate your help. I haven't been on the boards in quite a while but i remember you helping me in the past as well. Thanks again Mapes!