This is messy – really messy, and don’t even get me started on work, internal energy and all that nonsense (which is a catastrophic minefield of bizarre ‘conventions’), but I thought it was time to crystallize a few thoughts on this.
As usual, when studying Thermodynamics with my AP classes, I did a lab that involves a couple of reactions; one endothermic and one exothermic followed by the application of q = m c Delta T. The calculations associated with this lab and these reactions are very messy in two ways. Firstly the problem of deciding what actually constitutes ‘m’ in the equations is tricky. Gases are given off, single replacement reactions lead to the depositing of solids and reactants are in excess – what do we add together to get the correct ‘m’? Secondly, the problem of assigning signs correctly in order to end up with a positive sign for the endothermic reaction and a negative sign for the exothermic reaction is a prickly one. Most texts make much too difficult a song and dance about this IMO, and frankly you often run into the sign convention problem.
Frankly, the ‘mass issue’ is really a non-issue when it comes to the AP exam (as explained at the end of the document below), but the sign issue has the potential to be much less easy to clean up. This year, for the first time, I decided to create a short document that attempts to clarify things once and for all – I think it worked very well, and it seemed to be the clearest for the kids in many years.