So everyone knows about this method of making ice cream, cooling drinks, w/e. You add salt to ice and it lowers the freezing/melting point and this cools things below 0C. I understand why the freezing point is lowered and all that but I don't understand why this cools things down faster. So heres the thought experiment. You have ice at some temperature below 0, say -10C and you have two coke cans at 80F. divide the ice up into two piles and pour salt on one of them. What happens? Of course all this is a closed system ideal system with perfect thermal conductivity. we can consider the more realistic system later. The control experiment will come to some thermal equilibrium as dictated by [tex]m_1c_1 \Delta T=-m_2c_2 \Delta T[/tex] but thats not important right now. The experimental system will come to some thermal equilibrium at a lower temperature??? Knee jerk reaction is to say yes. After a little thought i still say yes. I think that because the aqeuous salt solution has a lower freezing point it you have the drink pouring heat into the high heat capacity lower temp water for longer because of the sooner transition to it, water, from ice. So the temperature of the water rises at the same rate ( maybe not ) as the control experiment but it starts rising from a lower temperature. I think the experimental system reaches thermal equilibrium faster because of Newton's law of cooling, the rate of change is proportional to the temp. differential, but I don't know how correct that DE is. Does it even apply when two bodies are changing temperatures or just a changing body and an ambient temperature? In addition to all this salt water apparently has a lower heat capacity than regular water but maybe not by much, I can't find it's specific heat. Supposing the heat capacities for both types of water are the same is my assessment of where they will reach thermal equilibrium accurate? I do not think it matters at which temperature the ice transition to water because that will be the same amount of heat lost by the drink no matter where along the time line it is. I think that since the transition from ice to water in the experimental system happens sooner, the drink is losing heat to the higher capacity water for longer. I mean this has gotta be true or else I wouldn't be able to make ice cream using this method. If someone could put up some math as to how I could describe the behavior of this system I would be much obliged.