Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference
between its own temperature and the ambient temperature (i.e. the temperature of its surroundings).
Newton's Law of Cooling Calculator
Newton's Law of Cooling equation is:
T_{2} = T_{0} + (T_{1} - T_{0}) * e^{(-k * Δt)}
where:
T2: Final Temperature
T1: Initial Temperature
T_{0}: Constant Temperature of the surroundings
Δt: Time difference of T2 and T1
k: Constant to be found
Newton's law of cooling Example:
Suppose that a corpse was discovered in a room and its temperature was 32°C.
The temperature of the room is kept constant at 20°C.
Three hours later the temperature of the corpse dropped to 27°C. Find the time of death.
(1)We use the observed temperatures of the corpse to find the constant k.
Δt = 3 (hrs)
T0 = 20 (°C)
T1 = 32 (°C)
T2 = 27 (°C)
k = (-1/Δt) * ln ((T2-T0)/(T1-T0)) = (-1/3) * ln ((27-20)/(32-20)) = 0.1797
(2)Assuming the temperature of a corpse at time of death is 37°C.
Now:
k = 0.1797
T0 = 20 (°C)
T1 = 37 (°C)
T2 = 32 (°C)
Δt = (-1/k) * ln ((T2-T0)/(T1-T0)) = (-1/0.1797) * ln ((32-20)/(37-20)) = 1.94
The death time is 1.94 hours before it was discovered.