Latent Heat: Calculating Final State of Ice/Steam Mix

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To determine the final state of a mixture of 20 g of ice at 0 degrees Celsius and 10 g of steam at 100 degrees Celsius, the heat exchange between the ice and steam must be analyzed. The heat gained by the ice as it melts and warms up must equal the heat lost by the steam as it condenses and cools down. The relevant equations include Q=mc(delta)T for temperature changes and Q=mL for phase changes involving latent heat. The discussion highlights the need to account for both the melting of ice and the condensation of steam to find the equilibrium state. Ultimately, the final state will be a mixture of water at a temperature determined by these heat exchanges.
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Homework Statement



Determine the final state when 20 g of 0 degree C ice and 10 g of 100 degree C steam are mixed together in an insulated container

Homework Equations



Q=mc(delta)T
Q=mL (L = latent heat)

The Attempt at a Solution



So, I know that I should set the heat change in ice equal to the heat change in steam, but how do I know what the heat changes are (including latent heat) if I don't know what the final state is?
 
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Sorry, the bold template part appears to have posted twice...I don't know why (I'm a new member)
 
Here ice melts and steam condenses. Both are in liquid state. Now proceed.
 
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