The rate at which ice melts depends on the rate at which thermal
energy can be delivered to it. Ice takes 80 calories per gram to break
the bonds between neighboring water molecules in the crystal so that
the water can flow.
The rate at which heat energy is delivered to a piece of ice
depends on many factors, such as the temperature of the air or water
you use, the thermal conductivity of the air and water, and if the air
or water are flowing. If there is no flow, then the ice cools off the
air or water which is close to it, and this slows down the heat
transfer to the ice because it is in contact with only cold air or
water. If the air or water flow, then the cold air or water are
constantly replenished with warm air or water, and then it is a
question of how much heat a volume of warm water or warm air can give
to the ice cube in a particular time.
If the air is very hot and/or flowing very fast and the water is
stationary, it is possible that the air may melt your ice first. I
will, for the moment, assume "normal" circumstances: an ice cube
floating in a large bucket of room-temperature water compared with an
ice cube hanging in the air on, say, a string, where the air is still
and also at room temperature.
Convection is a main determinant of how fast the ice will melt.
Cold air or water will sink, and be replaced by warmer fluid. Water has
a much higher heat capacity than air, and so it can deliver more
thermal energy at the same flow rate. The air may flow faster, but
usually not fast enough to match the difference in heat capacities.
One other effect that may be going on in the air experiment is
that some of the water which melts from the ice may then evaporate,
taking 540 calories per gram that otherwise could have been used to
melt more ice, further slowing the melting. If the air is very humid,
however, water may condense from the air onto the ice, liberating 540
calories per gram in the process, speeding up the melting.
(published on 10/22/2007)