>>9869586ok. the rate of heat flow is proportional to
Heat flow rate ~= k*A*(T1 - T2)
where A is the surface area, T1 and T2 are the different temperatures and k is a constant depending on the material.
Air, gas: k = 0.024 (fuck units, but this figure requires us to us C or K)
Water, liquid: 0.58
we want to determine if cool water or warm air will transfer heat faster. it would be interesting to see what temperature difference would cause them to melt at the the same rate. using 23 C as room temperature:
.024*A(23 - 0) = .58A(T1 - 0)
...
T1 = 0.95 C
so if the water is warmer than 0.95 C, the ice cube will melt faster in the water. this ignores that the air will cool as the ice melts, so the cold water will almost certainly melt the ice faster than the warm air.
