Figure-4.13 shows a water tank at a constant temperature. `T_(0)` and a small bodyof mass m, and specific heat S at a temperature `T_(1)` . Given that `T_(1) lt T_(0)`. A metal rod of length L, cross-sectional area A whose thermal conductivity is K is placed between the tank and the body to connect than. Find the temperature of body as a function of time. Given that the heat capacity of rod is negligible.

Explanation

As temperature of water tank is constant at `T_(0)` as it is very large, heat is conducted through the rod to the small body. If at an instant `t=t,` the temperature ofsmall body is 7, then the rate of heat flow through the rod can be written as
Equation-(4.16) is used for heat conduction is steady state and here as the heat capacity of the rod through which heat is conducted is negligible, it does not absorb any heat thus we can assume that it is always in steady state.
If on dQ amount of heat absorption, let the temperature of small body rises hydT, then we have
Now from equation (4.16)
Now integrating the aboveexpression in proper limits, we get