An Experimental Test of Newton's Law of Cooling

  To collect some data on cooling I took 2 cups of warm tap water in a measuring cup and inserted a photographic thermometer measuring temperature in °F. A clock on a nearby coffee maker was used to time the cooling with readings of the thermometer taken when the clock change its minutes readings. The data obtained is as follows,

Newton's Law of Cooling was tested by doing a curve fit for ΔT vs Δt to eliminate the constant term. A value for λ was assumed, B was estimated using the average value of ΔT divided by the exponential factor and the root mean square error for the data was calculated. Then  λ was varied to find the minimum rms error. In the formula below t is Δt, the elapsed time.

As time progresses cooling proceeds faster than expected from Newton's Law of Cooling which illustrates the problems one has with it over long periods of time.

Supplemental (3/16): The last 5 data points were excluded from the fit. There are only two variables in Newton's Law of Cooling so there's a problem with getting a curve with the proper curvature over extended intervals. There may also be other cooling mechanisms at work such as conduction, convection and evaporation which weren't included in the leaky vessel model of cooling.