# Stuck on integral!

1. The problem statement, all variables and given

integral of : (nRT)/(V-nb)dV from Vi to Vf

$$\int$$ $$^{Vf}_{Vi}$$ (nRT)/(V-nb)dV

I am really stuck on this one!
Do you need to move the denominator up first?

Last edited:

Assuming that everything except V is a constant for this problem, try the substitution

u = V -nb

Defennder
Homework Helper
You need to tell us which are constants and which are functions of V in this question. Otherwise, the problem becomes very simple when you factor nRT out.

Since the integral says "dV" doesn't that mean it only needs to be integrated with respect to the variable V while holding all other variables constant?

Assuming everything else is constant.

factor the nRT out. Let u = V-nb.
du/dv = 1 if nb is a constant.
This means that when u differentiate the denominator u get the numerator and its safe to straightaway ln the denominator.

I think it should be ln|Vf-nb| - ln|Vi-nb|

i might be wrong though.

Btw, is it just a practice question or are u doing this for chem? just curious. ;).

Also don't forget if you substitute u = V - nb, you must also write the limits of integration in terms of u.

I am doing these problems to touch up on my Calc for a class I am taking (physical chem)