Math Is Fun Forum

Oren

Guest

Plotting a function

Hello,

I am required to plot the function delta G = nRT [ xLnx + (1-x)ln(1-x) + Bx(1-x) ] as a function of x. This a problem from pchem literature and x denotes here a mole fraction ( limits between 0 and 1 ). B,n,R, and T = constants. The curves are shown in the book to have two minima and one maximum for B > 2.

My problem is trying to find these maxima / minima. The derivative should be zero but the algebraic equation seems not easy to solve.

d (delta G) / dx = 0

Lnx + 1 - 1 / 1-x -Ln(1-x) + x / 1-x + B - 2Bx = 0

Ln (x/1-x) -2Bx + B = 0

Now how exactly can this equation be solved inorder to determine the coordinates of the minima / maxima ?

thanks

Drew

Member

Registered: 2007-07-21

Posts: 2

Re: Plotting a function

Actually I did a research abou this myself and I found out in a physical chemistry book that logarithmic equations such as the above are called "transcendental equations", equations that do not have a solution in a closed form. The solutions are rather found using a mathematical software. I had that in mind although I thought there could be some sort of a mathematical trick or something that can be applied.

Oren