http://img842.imageshack.us/img842/7200/img0103iu.jpg
Mainly concerned with the first half of the page. You'll see that it derives for a system in contact with a constant-temperature, constant-pressure heat bath that the change in Gibbs entropy is always less than or equal to zero. Equality being for reversible transformations. A is the availability of the system AND its environment. However, I've honestly never understood something about this at all, and I've just tried to ignore it but it's come cropping up again for a different module for mine. Maybe it's something really simple.

The relation

[itex] dG = -SdT + VdP [/itex]

Is derived by considering the defition of Gibbs free energy. However, this formula is based on state variables, and hence works for all transformations. Right? It even confirms that for me in a different textbook of mine. So, in a constant temperature, constant pressure heat bath [itex] dT = 0, dP = 0 [/itex] always applies surely? There is no change in pressure of the system, there is no change in temperature. But then surely [itex] dG = 0 [/itex] for no matter what process? What is wrong in my reasoning?