Expert: Ahmed Salami - 5/16/2009

Question
Dear Sir,

There is an exercise in my mathematics book that asks me to find dV/dp of this formula: (p+(((n^2)a)/V^2))(V-nb)=nRT
The solution is ((-nRT/(v-nb)^2)+((2(n^2)a)/V^3))^-1

The question is: I find it a it difficult to understand why V-nb can be differenciated as a whole since the only letter susceptible of being differenciated are V and p. V-nb is a different value.

Thank you.

Answer
Hi Ignacio,
The expressions dont seem clear enough but i'm guessing you're wondering how d/dV[nRT/(V-nb)] = -nRT/(V-nb)^2
To make things look very easy, lets say K = V - nb and Q = nRT/(V-nb) so that Q = nRT/K and that we wish to find dQ/dV
Now,
dQ/dK = -nRT/K^2
and
dK/dV = 1
so,
dQ/dV = dQ/dK . dK/dV
     = (-nRT/K^2).1
     = -nRT/K^2
     = -nRT/(V-nb)^2
Notice that if n and b are constants, then both V and V-nb have the same rate of change.

You can always get back to me.

Regards