A state which produces heat while mixing with water
Answers
Entropy is a tricky concept at first but with some rigorous thought it becomes more and more intuitive.
When you mix hot and cold water they become inseparable in a closed system (closed to energy....we can still change the volume). Imagine putting a label on every single water molecule of the cold water and then picking them all out after you mix them with the hot water. You would have to supply quite a bit of energy in order to sift through all the molecules and separate them. (The second law applies to "closed" systems - which means to apply this correctly we cannot add energy to a system and thus sifting through and separating the molecules breaks the second law as it implies opening the system)
There are a couple ways to see that the entropy of the total system increases.
The first is simple: each volume of initially separated water has a greater volume to explore after mixing. Therefore the entropy goes up. This argument is best applied for 2 systems of water at the same temperature.
The second realization is that the maxwell-boltzman (MB) distribution of molecule speeds is asymmetric. When you mix two MB distributions of different average speeds the average speed of the resulting mixture is bounded by the average speeds of the two initial mixtures.
However, the number of molecules slower and faster in the mixture will not add geometrically.8 The asymmetric distribution will be of a different "shape" than the two initial distributions. Therefore the entropy increases after mixing two temperatures
Im not entirely sure but i think you are thinking of entropy as adding vectorally or being conserved.
I.e. the entropy of hot + entropy of cold = entropy of (hot + cold).....this is not true in general
Thanx