Argh!
All of this thermodynamics, or thermal physics (whatever it's called), is pretty messy stuff. That, and the fact that my partial derivative skills aren't so sharp are really frustrating me now. It's filled with experimental proportionality constants and some other screwy things. Curse it all!
Not quite sure why you'd be doing partials... that's usually held off until multivariable calculus.
Ditto.
This is just some physics thing that I've been doing on the side. I'm trying to come up with a usable theoretical prediction for the temperature of our electrolytic cells sans excess heat. Our current method for calculating excess power uses an experimental cell tested against a control cell. The only problem is that some of our data suggests that we may be producing excess in the control cell. The prof's trying to come up with an experimental design that would be guaranteed to produce no excess. He's thinking along the lines of an immersion heater. I can't find immersion heaters that run as low as 15W. Plus it would have to have a finely variable power output, and it might have to be acid resistant. A mathematical model would be a heck of a lot more convenient, but would undoubtedly be merely an approximation. I haven't figured it out yet. Chances are that it won't work, but it's fun to muddle with physics and calculus anyway.