Newton’s law of cooling (see Chapter 25) says that, if you put an object with initial temperature T0 K into an environment with a constant temperature A K (where A could be either greater or less than T0), then the temperature of the object can be modelled by T(t) = A + (T0 − A)e

−r t

, for some constant r. Often, scientists want to estimate r, which determines how fast the object cools down or heats up. For example, the rate at which a dead body cools can be used to estimate the time of death, something that is clearly important for forensic science.

a. Show that a plot of ln 

T(t)−A T0−A



against t gives a line with slope −r.

b. The parameter r for the cooling of human bodies was measured by Molnar et al (1969) and they obtained the data in Fig. 6.10.
Estimate r from these data for the two people. Be careful;
you need to calculate the slope of the line using the values of ln 
T(t)−A T0−A 
, not the values of T(t)−A T0−A .