Can anyone help me. I am very confused about the chemical potential. In the following equation dU = TdS - pdV + u dN, where u is the chemical potential it seems to me that if you add particles to a system you are increasing the energy of that system, i.e. the chemical potential is positive. Why is it then that the chemical potential is negative above a certain temperature (as can be seen by taken the derivative of the canonical partition function with respect to the number of particles (times -1/kT))? This would seem to suggest that as you add particles to a system, the energy of the system decreases!!!!!!