How do you increase a system's entropy without increasing the temperature? If entropy is the degree of disorder, won't more "disorderliness" means high kinetic energy, and the average energy of the particle (The temperature) will be higher?
or another way of saying is how to increase the heat energy without increasing temperature (since dQ=TdS)? Are we considering the potential energy between particles? I thought in the case of thermal physics, we would just consider elastic collision for every particle in the system?
And if this is the reason for temperature's independence of heat energy, can this be say so for entropy as well?