# Can Newton's law of cooling explain Mpemba effect? [duplicate]

Newton's Law of cooling states that the rate of loss of heat in proportional to the temperature difference. or $-dQ/dt = k(T' - T)$

Q → heat transferred, t → time, k → constant, T' - T → temperature difference.

## marked as duplicate by John Rennie thermodynamics StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Feb 13 '17 at 6:59

• Newton's Law of cooling doesn't "explain" anything. It's just a mathematical equation. For the Mpemba effect, it completely ignores phase changes (i.e. evaporation) and radiative heat loss. Even in situation where it is relevant, the physics is what determines the value of the "constant" $k$ - and in most real world situations $k$ is not constant! – alephzero Feb 13 '17 at 11:20
Actually Newton's Law of cooling would predict that cold water would freeze faster than hot. If the hot water is a temperature $\text{T}_\text{H}$ and the cold water is at $\text{T}_\text{C}$ then the hot water would have to cool through temperature $\text{T}_\text{C}$ to reach the freezing point. So hot water should take longer.