Why do dP/dT, dT/dV and dV/dP multiply to -1 for an ideal gas?

[Niles]

Homework Statement

The law for an ideal gas is given by P = n*R*T/V. In our case, n and R are constant, so P = f(V,T).

I have found dP/dT, dT/dV and dV/dP. I have to find the result when these three differentials are multiplied with each other.

The Attempt at a Solution

I get -1 - can you guys confirm this? And what does this mean?

 

[Hurkyl]

Looks right to me. This is true for any three variables related by a differentiable function.

 

[Niles]

I see.. does it have any specific meaning for an ideal gas?

 

[Niles]

I have searched Wikipedia - I haven't found anything. Can you help?

 

[Hurkyl]

I cannot think of any meaning that goes beyond the literal interpretation of the operations.

e.g. it suggests that, at least on tiny scales, you can compute the relationship between P and V along an isotherm by instead looking at how T and P relate along an isochore and how T and V relate along an isobar.

 

[learningphysics]

Found this link on wikipedia. But it doesn't go through much except an informal derivation:

http://en.wikipedia.org/wiki/Cyclic_chain_rule