Total heat gained by ice is equal to the total heat lost by steam.
For ice to completely convert into water, heat required is
m1Lf=1×80=80 cal For steam to completely convert into water, heat released is
m2Lv=1×540=540 cal Hence, first 80 calories will not be enough for the steam to condense completely. Now, to convert melted water to
100∘ C from
0∘ C, heat required is
m1s(100−0)=1×1× 100=100 cal So, total energy required to heat ice to water
100∘ C is
100+80=180 cal. Hence, even this amount of energy is not enough for the steam to condense completely. Hence, the final temperature of the mixture will be
100∘ C.
Note- finally the mixture will consist of both steam and water at
100∘ C.