Question

P = (nRT)/(V-nb) - (an^2)/V^2)

Find dP/dV

Answer 1

I think I'm supposed to use the quotient rule here, but I don't really know how D:

Answer 2

If this is a closed system, then n is constant. The temp (T) could also be held constant as long as not otherwise instructed. You can relate this to a function of the following form (1/x +1/x^2) and take the derivative. With all other items in the equation are held constant, it is a simple derivative.

Answer 3

I'm not quite sure I understand that. Could you explain it a bit more thoroughly?

Answer 4

The only variables will be V. n is moles, T is temperature, R is a gas constant and a and b are constants also. Lets look at it this way. I will define nRT as c1 and an^2 as c2 and nb as c3 all of which are constants so P = (nRT)/(V-nb) - (an^2)/V^2)......>P=c1/(V-c3) -c2/V^2. To take the derivative of c1/(V-c3) do a U substitution by letting V-c3=U so the derivative will of c1/(V-c3) will be -c1/(V-c3)^2. The other derivative should be easy (c2/V^2). The reason I created c1, c2 and c3 is so we can see that they are constants which makes taking the derivative a little easier. After we have this all solved we can substitute back into the constants we created. I hope this helps