Question

The result obtained by combining first and second laws of thermodynamics is

Answer 1

TdS Relations

Consider the first law:

dQ - dU + dW (1)

For a reversible process:

dQ = TdS & dW = pdV

TdS = dU + pdV (2)

But

H = U +PdV

So that

dH = dU + pdV + Vdp (3)

Substituting 3 into 2 we get:

Tds = dH - Vdp (4)

Note:

Equations 2 and 4 were derived for a reversible process and so they can be integrated for a reversible process only. But they deal with properties ie. They only depend on end state so the change in properties during a given change of state are the same for an irreversible process as for a reversible process. Therefore they can be used for irreversible process as well.