Pails of hot and cold water are set out in freezing weather. Explain how (a) if the pail have lids the cold water will freeze first, but (b) if the pail don’t have lids it is possible the hot water freezes first.

As the water cools it will eventually develop convection currents and a non-uniform temperature distribution. At most temperatures, density decreases with increasing temperature, and so the surface of the water will be warmer than the bottom: this has been called a "hot top." Now if the water loses heat primarily through the surface, then water with a "hot top" will lose heat faster than we would expect based on its average temperature. When the initially warmer water has cooled to an average temperature the same as the initial temperature of the initially cooler water, it will have a "hot top", and thus its rate of cooling will be faster than the rate of cooling of the initially cooler water at the same average temperature