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Topic: Proving Charles' Law using Enthalpy.  (Read 3225 times)

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Offline PKemNoob

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Proving Charles' Law using Enthalpy.
« on: February 18, 2013, 06:37:49 AM »
Hi, I am in a pchem course and I am having trouble with this question:

Starting from the expression dH = dU + d(PV) show that for an ideal gas V1/T1 = V2/T2 if the pressure is kept constant. There is supposed to be some integration involved.

I know that CpdT = CvdT + nRdT  :rarrow: dH = dU + d(PV), but where do I go from here?


Offline UG

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Re: Proving Charles' Law using Enthalpy.
« Reply #1 on: February 19, 2013, 02:03:59 AM »
You could start by going dH = dU + PdV + VdP, cancel out the last term, and replacing dH and dU with heat capacity terms

Offline PKemNoob

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Re: Proving Charles' Law using Enthalpy.
« Reply #2 on: February 23, 2013, 05:01:49 AM »
Umm yeah, that's exactly what I did in my original post to start out, as you can see above.

Offline UG

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Re: Proving Charles' Law using Enthalpy.
« Reply #3 on: February 23, 2013, 05:37:40 AM »
Ok, you can replace dH with CpdT, can you think how to replace dU for an ideal gas?

Offline PKemNoob

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Re: Proving Charles' Law using Enthalpy.
« Reply #4 on: February 23, 2013, 05:55:48 AM »
like it says in my original post: dh is CpdT, dU is CvdT and d(PV) is nRdT .:. CpdT= CvdT + nRdT.

Offline UG

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Re: Proving Charles' Law using Enthalpy.
« Reply #5 on: February 23, 2013, 06:43:31 AM »
Oh right, sorry, my brain wasn't clicking there.

I know that CpdT = CvdT + nRdT  :rarrow: dH = dU + d(PV), but where do I go from here?
So then CpdT - CvdT = nRdT = PdV (since dP is 0)
Integration on both sides give you the Ideal Gas Law, with n, R and P all constants. This can be simplified to Charles' Law. Don't know if this is satisfactory proof for you :-\

Offline PKemNoob

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Re: Proving Charles' Law using Enthalpy.
« Reply #6 on: February 23, 2013, 08:51:24 AM »
I've tried taking that approach before but it lead me only to bad places... perhaps I am doing the integration wrong??? Can you work it step by step so I can compare it to my attempts at deriving it?

Offline PKemNoob

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Re: Proving Charles' Law using Enthalpy.
« Reply #7 on: February 23, 2013, 09:12:04 AM »
Nevermind, I got it... thanks, idk why I didn't see that.. maybe bc i dont sleep lol

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