Change of variables in heat equation

[tickle_monste]

dT_B/dt = -k(T_B-T_M).
T_M is held constant.

(T_B-T_M) = Q, so:
dT_B/Q = -kdt.

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

 

[HallsofIvy]

dT_B/dt = -k(T_B-T_M).
T_M is held constant.

(T_B-T_M) = Q, so:
dT_B/Q = -kdt.

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

That's a simple "linear" substitution. Since T_B= Q+ T_M, dT_B/dt= dQ/dt. Your equation becomes just dQ/dt= -kQ.

 

[tickle_monste]

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