the 0th law of thermodynamics states that if 2 systems A and C are in thermodynamic equilibrium with a 3rd system B, then A and C are in thermodynamic equilibrium. in other words, if A has the same temperature as B and B has the same temperature as C, then A has the same temperature as C. I am a little confused with thermometers however. Let's say you use a thermometer to measure some very hot water. The thermometer and the very hot water are the 2 systems and when they come to thermodynamic equilibrium we get a reading. Then lets use the thermometer to measure some very cold water and we get a reading as well. The readings are obviously different. But if the thermometer is in thermodynamic equilibrium with the hot water and cold water then by the 0th law shouldn't the hot and cold water be in thermodynamic equilibrium with eachother? but that must mean they have the same temperature which makes no sense at all. this has been confusing me greatly. can someone help explain this? thanks.