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**Equation apply to reversible only or not??**

My thinking must be faulty somewhere, but I can't work out whats gonig on...

The equation

**Tds = du + pdv**and

**du = dq + dw**

are supposed to be valid for all processes right?

yet

**dw = -pdv**only for reversible cases, yes?

So how do you prove that

**du = Tds + fdx**

given that

**fdx = dw**(for a stretched wire) if you don't know if its a reversible process?

As

**fdx = dw**can only be equated with the

**-pdv**if its reversible.

[or similarly,

**ydA**in place of

**fdw**for the surface tension of a droplet. Are you just supposed to know these are reversible?]

Secondly, is Cp, 'heat capacity at constant pressure' independent of pressure?

Anybody know the answers??