NVM - turns out prof wrote their equation down wrong. I was sure that, for heating, it should be dT/dt = k(T-A), and that's what it turns out to be (unless somebody wants to contradict that?)
Cheers anyway.
Hello all,
I thought I had this nailed when a little confusion reared its ugly head. When dealing with objects that are cooling (coffee etc), I want to use dT/dt = -k(T-A) where A is ambient temp, T is temp of e.g. coffee.
Now the dead body in the sauna problem, of a thing heating up. What equation do I use here? dT/dt = k(T-A)? dT/dt = k(A-T) (Which is effectively dT/dt = -k(T-A)?
Any help appreciated, but please bear in mind I have an exam on this tomorrow!
Your expression equates to dT/dt = -k(T-A) for a scenario of warming. I was told that it matters that you use a negative k for cooling and a positive k for heating (at least by one source) - something like one produces a converging exponential and one produces a diverging exponential... unless I'm getting muddled with formulae for compound interest - which could well be the case.
Reeto - well that ship has sailed now anyway. The exam was this morning. There was a differential equation question about sprouts, but I think I got it right. Most of the rest of the exam was, however, a complete bugger. I ultimately got stumped by a question on so-called 'homogeneous differential equations', which appear to involve some kind of substitution of some function of x and y for z. But since it wasn't the basic stuff I've seen before on that topic, it was all way too much for my tired mind (no sleep).