Solving the Steam & Ice Temperature Problem - Need Help!

physicnow
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I have this problem, but I could not understand. pls help

Steam at 100 degree celsius is added to ice at 0 degree celsius. The mass of the steam is 10 g and the mass of the ice is 50.0 g. What is the final temperature of the mixture?

thanks a lot.
 
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You need to know the energy (per kg) lost by steam turning into water = heat of vapourisation.
The energy (per kg) it takes to melt ice = heat of fusion
The energy needed ( per kg per kelvin ) needed to heat water.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.

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