You are a forensic doctor called to a murder scene. When the victim was discovered, the body temperature was measured and found to be 20°C. You arrive one hour later and find the body temperature at that time to be 18°C. Assuming that the ambient temperature remained constant in that intervening hour, give the police an estimate of the time of death. (Take 37°C as normal body temperature.)
Newton's law of convective cooling can be written in the form
dT/dt = -C(T - Ta)
where C is a constant that involves the heat capacity and cooling coefficient, and Ta is ambient temperature.
The solution to the differential equation is
Newton's law can be written in the form
dT/dt = -C(T - Ta)
where C i
My answer seems to have been not fully uploaded. Sorry about that. Computer problems here.
Shame about your computer. Don't want to die wondering ;)
The solution is
(T-Ta) = (To-Ta)e^-Ct
Where To = 37 C and Ta = ambient temperature
Your two data points give you two equations in three unknowns: t (when reported), Ta and C. The time of second measurement is t + 1 hr. More information is needed to make an estimate. You would need the value of ambient temperature or the Newton heat loss coefficient C