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. |
