A blacksmith wishes to cool his hot piece of steel as rapidly as possible. He has a bucket of ice-water and a bucket of oil (at room temperature). Which bucket should he dump his steel into?
OK that solution posted up there is DEFINITELY wrong. I won't go into heat transfer principles or quote equations, which I could do, but just present simple logic and historical evidence.
We know that raising a liquid to above boiling requires more energy than simply raising its temperature. It is safe to assume the blade is of sufficient temperature to boil the water (ask any blacksmith/metallurgist/metal sculptor and he'll tell you its a lot hotter than 100 deg C that is required to mould metal-its more like 600 deg C depending on other factors). The latent heat of vaporisation for water, the property which defines the energy required for the liquid to change phase, is considerably larger than the energy required to heat oil to any temperature below its boiling point, and the boiling point for oils is in the range of over 300 deg C which means that oil will still be being raised degree by degree according to its specific heat capacity, well after the water would have boiled and in so doing created a mechanism to remove heat at a higher rate. The stuff about the creation of a layer around the blade might be plausible (though I've never heard of such a consideration), but that layer will dissipate far sooner than it would take the oil to get to boiling. It would really be a transient condition if anything.
Anyway you could argue many ways around what I said because I've failed to give those numbers associated with eqch phenomenon, and I don't really have the inclination to go delve into heat transfer rates and specific heat capacities and so forth....BUT
I know for a fact the solution is certainly wrong without any hesitation whatsoever, since in the process of making steel, water quenching is used to produce high martensite (brittle) steels because the faster a steel is cooled, the more martensite is formed.
And one of the ways to cool down steels at reduced rates (thus making less brittle steels), used as a standard everywhere, and common knowledge for any mechanical engineer, is oil-quenching....
(Air cooling is used to form even lower martensite steels)