Internal Energy of a Van der Waals Gas
So I have this question. Im able to derive the first part, however integrating the equation is for some reason stumping me.
So I took dV over to the RHS, giving du=a/v^2 dv. Which I promptly integrated and got U=(-a/v) + c where c would just be an integration constant correct? But how am i supposed to show that c=3RT/2. I get that this is the U for an ideal gas, but Im not sure if that's relevant or not.
Original post by Eremor
So I have this question. Im able to derive the first part, however integrating the equation is for some reason stumping me.
So I took dV over to the RHS, giving du=a/v^2 dv. Which I promptly integrated and got U=(-a/v) + c where c would just be an integration constant correct?
So I have this question. Im able to derive the first part, however integrating the equation is for some reason stumping me.
So I took dV over to the RHS, giving du=a/v^2 dv. Which I promptly integrated and got U=(-a/v) + c where c would just be an integration constant correct?
Incorrect, since you are integrating a partial derivative where T is held constant. So the most general term with T that can differentiate back to 0 in this case gives you:
To check that, find from that expression.
But how am i supposed to show that c=3RT/2. I get that this is the U for an ideal gas, but Im not sure if that's relevant or not.
I'm not sure what they want here, but:
1. this isn't an ideal gas since in an ideal gas, particles have no volume
2. consider what would happen if - this would bring you closer and closer to the ideal gas state, since the particle volume eventually becomes negligible w.r.t V. And what would the energy tend towards?
Original post by Eremor
Ah, i see what you mean.
Thankyou for the help!
Thankyou for the help!
You thanked me too soon. I've realised that I made a mistake above - when you integrate, you'll end up with:
where is some arbitrary function of T. So you need to do some more work to justify the linearity in T. I'll have to think about this later, when I get the time.
[edit: there's no more to justify - just apply the reasoning that I mentioned earlier - that gives you the whole term]
(edited 8 years ago)
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