[PKemNoob]

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  dH = dU + d(PV), but where do I go from here?

[UG]

You could start by going dH = dU + PdV + VdP, cancel out the last term, and replacing dH and dU with heat capacity terms

[PKemNoob]

Umm yeah, that's exactly what I did in my original post to start out, as you can see above.

[UG]

Ok, you can replace dH with C_pdT, can you think how to replace dU for an ideal gas?

[PKemNoob]

like it says in my original post: dh is CpdT, dU is CvdT and d(PV) is nRdT .:. CpdT= CvdT + nRdT.

[UG]

Oh right, sorry, my brain wasn't clicking there.

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

So then C_pdT - C_vdT = 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

[PKemNoob]

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?

[PKemNoob]

Nevermind, I got it... thanks, idk why I didn't see that.. maybe bc i dont sleep lol