Fing (�ÝV/�Ýp)_T,n
given pV = nRT(1 + (B/V) + (C/(V^2)) + (D/(V^3)) )
I know how to do partial differentiation, but I have no idea how to rearrange this for V
Sorry that didn't come out clearly. The first part is meant to say Find and then the partial differential dV/dp
To rearrange the equation for the variable V, let's first isolate the terms containing V on one side of the equation.
Start with the equation:
pV = nRT(1 + (B/V) + (C/(V^2)) + (D/(V^3)))
Step 1: Divide both sides of the equation by p
pV/p = nRT(1 + (B/V) + (C/(V^2)) + (D/(V^3)))/p
Simplifying,
V = nRT(1 + (B/V) + (C/(V^2)) + (D/(V^3)))/p
Step 2: Take the reciprocal of both sides
1/V = p/(nRT(1 + (B/V) + (C/(V^2)) + (D/(V^3))))
Step 3: Multiply both sides by V
(1/V) * V = (p/(nRT(1 + (B/V) + (C/(V^2)) + (D/(V^3))))) * V
Simplifying,
1 = pV/(nRT(1 + (B/V) + (C/(V^2)) + (D/(V^3))))
Now you have rearranged the equation for V.