The final result, ice at 0 °C and steam at 100 °C, will be liquid water at a temperature close to the melting point of ice, which is 0 °C.
When ice and steam are mixed together, the heat energy in the steam will be transferred to the ice, causing the ice to melt and the temperature of the resulting water to rise. The amount of heat energy required to melt a given mass of ice is known as the heat of fusion, and for water, it is approximately 334 J/g. The heat of fusion is the amount of energy required to change the phase of a substance from a solid to a liquid, and it is typically a relatively small amount of energy compared to the heat of vaporization, which is the amount of energy required to change the phase of a substance from a liquid to a gas.
As the heat energy is transferred from the steam to the ice, the temperature of the water will rise until it reaches the melting point of ice. At this point, the ice will have completely melted and the temperature of the water will remain constant until all of the steam has been condensed into water. The final result will be liquid water at a temperature close to the melting point of ice.
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