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## Homework Statement

Show that (du/dv)

_{T}= T(dp/dt)

_{v}- p

## Homework Equations

Using Tds = du + pdv and a Maxwell relation

## The Attempt at a Solution

I've solved the problem, but I'm not entirely sure my method is correct.

Tds = du + pdv ---> du = Tds - Pdv

- Using dF=(dF/dx)

_{y}dx +(dF/dy)

_{x}dy

du=(du/dT)

_{v}+(du/dv)

_{T}dv

- Therefore Tds - Pdv = (du/dT)

_{v}+(du/dv)

_{T}dv

- Divide by dv:

(du/dT)

_{v}dT/dv + (du/dv)

_{T}= T(ds/dv)

_{T}- p

**Now, to get the right answer, this term:**

(du/dT)

must equal zero, but I'm not sure why - please can somebody explain?

(du/dT)

_{v}dT/dvmust equal zero, but I'm not sure why - please can somebody explain?

Then you simply insert Maxwell relation -(ds/dv)

_{T}= -(dp/dT)

_{v}

and rearrange to get the correct answer.

Many thanks for any help!