# Keeping things together can raise a problem!

In a container of negigibe heat capacity, $$200$$ g of ice at $$0^{\circ}C$$ and $$100$$ g steam at $$100^{\circ}C$$ are added to $$200$$ g water that has temparture $$55^{\circ}C$$. Assume no heat is lost to the surroundings and the pressure in the container is constant $$1.0$$ atm. Now if the final temprature of the system and the mass of total water present at this temprature can be represented as $$A$$ (in degree Celsius) and $$B$$ (in grams), find $$A+B$$.

Details and assumptions

Latent heat of fusion for ice = $$80 \text{ Cal/g}$$, Latent heat of vaporization for water = $$540 \text{ Cal/g}$$ and specific heat of water = $$1 \text{ Cal/(g K)}$$

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