Question #42154

A small solid body of heat capacity $C = 20 \text{ J/K}$ is initially at a temperature $T_0 = 0^\circ\text{C}$. It is connected to two large heat baths maintained at temperatures $T_1 = 100^\circ\text{C}$ and $T_2 = 0^\circ\text{C}$ through two distinct uniform rods of negligible heat capacity. The thermal resistances of the rods are $R_1 = 5 \text{ K/W}$ (connected to $T_1$) and $R_2 = 20 \text{ K/W}$ (connected to $T_2$). The connections are made simultaneously at $t = 0$. Assuming no heat loss to the surroundings, what is the rate of heat flow from the $100^\circ\text{C}$ bath into the first rod at time $t = 80 \ln 2 \text{ s}$?