Two character heat problems

We have looked at a number of simple calorimetry problems and some that were more complex because they involved multiple steps.

Another way that calorimetry problems can be more complex is if they involve more than one “character.” That is, the problem involves one thing giving away heat and one thing taking heat.

A simple example of this is when you place a cold spoon into a cup of hot coffee. You know, of course that the spoon gets hot. Knowing what you now do about heat, you realize that the spoon gets hotter because it is taking in heat. It makes sense then that the heat must be coming from the coffee and as a result, the coffee will be getting colder.

The key to understanding these problems is to recognize that the amount of heat given away by one “character” (in this case – the coffee) must be the same as the amount of heat taken in by the other “character” (the spoon).

We also need to remember that when something is losing heat, the value of q is negative and when something is gaining heat the value of q is positive. Therefore these two values cannot be equal unless we change the sign on one of them.

This will leave us with the general formula:

Some examples can be found here: