Thermodynamics- pV^n = constant.

AI Thread Summary
The discussion revolves around solving for the variable n in the equation pV^n = constant, given specific initial and final pressures and volumes of a gas. The user initially struggles with rearranging the equation and isolating n, expressing frustration over the complexity of the logarithmic manipulation. After guidance from another forum member, they clarify the correct logarithmic approach, leading to the equation ln(P1) + n*ln(V1) = ln(P2) + n*ln(V2). This realization helps the user feel more confident in their understanding and problem-solving skills. The exchange highlights the importance of collaborative learning in tackling thermodynamics problems.
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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.
 
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The logarithm function turns exponential factors into multiplicative factors...
 
Mapes said:
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 :-p
 
You're not taking the logarithm correctly.
 
Mapes said:
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)
 
Better!
 
Mapes said:
Better!

Awesome, thanks Mapes! How did I not see that :blushing:

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!
 
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