dT/dt = k(Tsurr-T)
Says that the
rate at which the
temperature of a
body changes is
proportional to the
difference between the body's temperature and that of the
surroundings. When
Tsurr is taken to be a
constant (and not a
function of time), this law is only an
approximation, since the temperature of the body effects that of the surroundings, not just the other way around. The latter effect is usually
neglected, since the 'surroundings' are generally much larger than the body in question. (The surroundings act as a '
sink'.)
But, nevertheless, this
law is only correct for substantial temperature differences if the
heat transfer is by forced
conduction or
convection.
As with all members of this family of
differential equations, it leads to some sort of
exponential function. In this case, it's the temperature difference which falls
exponentially to
zero.