I have a question regarding phase transitions: It all textbook I've seen the assumption that dP=0 during a phase transition (so that for example dH=TdS is true during a phase transition). Could anyone explain why this should be true? I guess I could relate this question to a question I had during intro (Halliday) Physics: Why can we assume that temperature is constant during a phase transition? (Back then I imagined that after a certain point putting in energy to get the molecules to move faster does not really lead to a substantial increase in entropy, so that the rigid structure e.g. of the solid or the liquid has to be broken down, so that subsequent temperature increase would actually lead to a decent entropy increase, at the cost of reduced internal energy.) And then the final related question: Why can't the pressure and temperature both change by "wandering" along the phase-transition line?