How Does the Reciprocal Nature of Partial Derivatives Apply to Ideal Gases?

ramsharmjarm
Messages
7
Reaction score
0

Homework Statement



Prove that
(∂P/∂V) n,T = 1/(∂V/∂P) n,T

n and T are supposed to mean that theyre just constants

Homework Equations



Ideal Gas

PV=nRT

The Attempt at a Solution



I tried

(∂P/∂V) n,T= ∂nRT/v/∂V = ∂nRT/V ∂V

then I am stuck here
 
Physics news on Phys.org
ramsharmjarm said:

Homework Statement



Prove that
(∂P/∂V) n,T = 1/(∂V/∂P) n,T

n and T are supposed to mean that theyre just constants

Homework Equations



Ideal Gas

PV=nRT

The Attempt at a Solution



I tried

(∂P/∂V) n,T= ∂nRT/v/∂V = ∂nRT/V ∂V

then I am stuck here

Why are you stuck? n, R and T are constant. Move them outside the differentiation. Now you've just got ∂(1/V)/∂V. What's that?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top