# Thermodynamics: Show that the two relations give Pv = RT

1. Oct 1, 2012

### karan4496

1. The problem statement, all variables and given/known data

For an ideal gas the slope of an isotherm is given by

(∂P/∂v) constant T = -P/v

and that of an isochore is

(∂P/∂T) constant v = P/T

Show that these relations give Pv = RT

2. Relevant equations

Pv = RT

3. The attempt at a solution

I have never worked with partial derivatives before encountering this problem so I am unfamiliar with the rules and operations involved. I tried setting them equal, adding them to each other but I just don't know where I am going.

2. Oct 1, 2012

### voko

You can treat each of the equations as an ordinary differential equation where the independent variable is V and T respectively. When you solve them, you will have two constants. But these constants must be then functions of the "constant" variable, T and V respectively. Then you should be able to find those functions and get the ideal gas law.

3. Oct 3, 2012

### karan4496

Ok so I got up to this step.

dP = -P/v dv + P/T dt

Im unsure of how to proceed from here

4. Oct 3, 2012

### vela

Staff Emeritus
Divide by P and then integrate.

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