Question

Show that (product of these three partial derivatives) = -1.

http://f.imgtmp.com/GKVay.jpg

Answer 1

take the partials of the equation

PV=mRT

Answer 2

Zarkon: What will that do?

Answer 3

Zarkon: or are you asking me to give it to you?

Answer 4

I'm saying that is what you need to do...the partials are not that hard.

Answer 5

\[T=\frac{PV}{nR}\to\frac{\partial T}{\partial P}=\frac V{nR}\]\[P=\frac{nRT}V\to\frac{\partial P}{\partial V}=\frac{-nRT}{V^2}\]\[V=\frac{nRT}{P}\to\frac{\partial V}{\partial T}=\frac{nR}P\]\[\frac{\partial T}{\partial P}\times\frac{\partial P}{\partial V}\times\frac{\partial V}{\partial T}=\frac V{nR}\times\frac{-nRT}{V^2}\times\frac{nR}P=-\frac{nRT}{PV}\]

Answer 6

Zarkon: I don't find partials hard it's just I don't know what I am being asked to do specifically. TuringTest: Am I supposed to notice that PV = nRT is the ideal gas law and then say that -nRT/PV = -1 is correct because of this?

Answer 7

seems that way

Answer 8

TuringTest: Let me just process what you typed but I get the overall "image" :)

Answer 9

Oh, seems really simple!

Answer 10

yep, you were probably overcomplicating it

Answer 11

Thanks!

Answer 12

Problem: This method only shows that it works if it's an ideal gas but we are trying to show that it works for all systems. Apparently, I need to use the implicit function theorem. How do I do this?

Answer 13

Hm... I don't know about that theorem. I bet Zarkon does though. You could try to message him.

Answer 14

I think I'm about to figure it out anyways. But, for future reference, how do you message someone?

Answer 15

highlight their picture and you can become their fan
once you are their fan you can send a 'fan message', which works as a private message system.
very handy for getting help on more advanced problems