What cools hot water more - ice or cold water?

What cools water more.....

One might assume that adding ice to hot water will cool it more than adding "cold water", but you should define your terms. What you have asked is fraught with interpretation and different ways of adding ice and cold water, and will have have no clear outcome until the specifics are nailed down.

The gist of the question comes down to the latent heat of fusion and that heat from the hot water is needed to melt the ice at 0C so that the "ice water" will continue to cool the hot water until equilibrium is reached.

• In both cases the hot water should have a known volume and temperature.

• The added cold water should have a known temperature, and the amount should be less than the amount of hot water. For instance, adding 200g of water at 5C to 200g of water at 70C might cool it more than placing a 5g chip of ice in 200g of water at 70C.

• The added ice should have a mass and an initial temperature specified so that the amount of heat gained in warming the ice, melting the ice, and heating the "ice water" to equilibrium can be determined.

• If there is to be any agitation of the water (stirring) then it must be done in both cases.

Adding the cold water will cool the hot water faster, because it mixes faster. Adding the ice will cool it down to a lower temperature, but it takes longer.