In class today, Dr. Lavelle explained how a burn from steam hurts more than a burn from water. To understand this, we must know that the
(liquid --> gas) is approximately 41kJ/mol. (This value can be found in a chart.)
We are assuming that your skin is less than 100 degrees, the temperature of boiling water. In his example, it was stated that for equilibrium to be reached between the temperature of the water and the temperature of skin, heat from the water is transferred to and absorbed by the skin. The amount of heat transferred for this liquid is 5kJ.
When steam at 100 degrees hits your hand, before its temperature can reach the temperature of your hand, it has to go through a phase change (vapor/gas --> liquid). Then once it is a liquid, it is the same as if boiling water at 100 degrees touched your hand. (It must first go through a phase change before the temperature can decrease.) Therefore, in the case of steam you need to add the
(41kJ) to the 5kJ from above. This totals 46kJ.
To answer your second question, the reason the phase change from water to steam is longer than ice to water is just due to the fact that more heat is required to break the bonds of water than that of ice.