# helmholtz free energy of a polymer

You have a polymer chain of $N$ units, which is represented by $N$ independent springs in series. The springs are Hookean, with spring constant $L$, and the end to end vector is $\mathbf r$. So the energy of the spring is $$\frac{L\mathbf r\cdot\mathbf r}{2}.$$

Neglect kinetic energy contributions. There is one state per volume $W$ in $\mathbf r$-space.

Calculate the Helmholtz free energy of the polymer (you need to integrate over all possible values of the three-component end to end spring vectors.)

I have no idea how to set this up, what three integrals? How do they lead to the free energy?

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What university do you study at? – Mew Dec 19 '12 at 6:28
UDel, why do you ask? – Alex Trent Dec 19 '12 at 6:31
you wouldn't happen to know how to approach this, would you? – Alex Trent Dec 19 '12 at 6:36
because kinetic energy is being neglected, this isn't a random stepping problem - so i don't know how to approach it – Alex Trent Dec 19 '12 at 6:36
I just asked because some of the questions were similar to what I remember from uni. – Mew Dec 19 '12 at 6:37