Chamber A has an internal temperature of TA degrees. Chamber A is submerged in the fluid contents of Chamber B, which has an internal temperature Tp degrees. Chamber B is in turn submerged in the fluid contents of Chamber C, which has an internal temperature Tc. Finally, Chamber C is submerged in the fluid contents of a large tank with temperature Te.
Let a, b, and c represent the constants of proportionality for the rate of heat transfer through the walls of Chambers A, B, and C. Complete the system below to model this situation:
dTA/dt = -a(TA - TB)
dTB/dt = 2b(TB - TC)
dTc/dt = 0
dTC/dt = b(TB - TC) - c(TC - Te)