- #1
grandpa2390
- 474
- 14
Homework Statement
begin with ##H = U+PV##. Manipulate it into the form: ##(\frac{∂H}{∂U})_P##
hint: you might find the resulting expression from part a useful)
the resulting expression that I found was ##(\frac{∂U}{∂V})_P = \frac{C_V}{V*a} + π_T##
Homework Equations
##π_T## = ##(\frac{∂U}{∂V})_T = T(\frac{∂P}{∂T})_V - P##
##a = \frac{1}{V}(\frac{∂V}{∂T})_P##
equation of state
##dU = TdS - PdV##
##dH = TdS + VdP##
The Attempt at a Solution
I was able to solve part a. what is throwing me off is that the terms are not partials, but I need to manipulate it so.
What I tried was to say that ##(\frac{∂H}{∂U})_P = dU##
but... I don't think that's right, and if it is, I don't know where to go from there...
you start with dU in the first equation. ##dU = C_VdT + π_TdV## and the resulting equation is what I wrote above... Maybe I plug that in for dU? but then what about the hint saying to do something with the resulting equation.
maybe plug in the dU and dH... but then again, I keep coming back to that hint...
edit: I forgot to write what a is equal to. adding that now
edit2: ok it's there. I am pretty sure I have everything now. If I am missing something, just ask. I'll try my best.
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