# Change of variables in heat equation

1. Dec 4, 2009

### tickle_monste

dTB/dt = -k(TB-TM).
TM is held constant.

(TB-TM) = Q, so:
dTB/Q = -kdt.

How would I change this equation so that instead of integrating wrt to TB, I can instead integrate wrt Q?

2. Dec 4, 2009

### HallsofIvy

Staff Emeritus
That's a simple "linear" substitution. Since TB= Q+ TM, dTB/dt= dQ/dt. Your equation becomes just dQ/dt= -kQ.

3. Dec 6, 2009

### tickle_monste

Wow, I really should've been able to do that myself. Thanks a lot though, thats a big help