## Heat Flow

After death, the human body no longer generates heat of its own accord. The approximate rate at which it moves toward the ambient temperature is given by Newton's Law of Cooling, which states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surrounding environment. This can be stated as a differential equation...

...where *T(t)* is the temperature of an object at time *t*, *M* is the temperature of the surrounding environment, and *k* is a constant. The equation is solved by the function...

...where if *t* is the time elapsed since death, then *T _{0}* is the body temperature at time of death (

*t = 0*). Note that if two temperature readings are taken on a corpse at two different times, it's possible to determine

*k*and the time of death.

^{6}