The trick on mixing various hot and cold components of a system is to remember that ALL the processes must balance out completely. All the hot components must cool down (lose joules) by exactly the amount that the cold components heat up (gain joule). This can be written algebraically:process1 + process2 + process3 + etc... = 0Where each process is an equation for heat representing one of the segments on the heating diagram which is show below. Let’s assume this diagram is for water. Segment A to B is for heating ice to 0°C, B to C for melting ice to water at 0°C, C to D for heating water from 0°C to 100°C, and so on...This ultimately leads to a rather LARGE algebraic equation with lots to keep track of, especially the signs on temperatures. Not to mention you have to know where you will end up on the diagram to truly set up the processes correctly.An easier way is to realize that the answer is path independent and I can imagine it happening anyway I see fit as long as a quantify all steps. So I prefer to pull ALL COMPONENTS of the problem (whether
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