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Final temperature of the mixture of steam and ice

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Steam at 100C is added to ice at 0C.The mass of the steam is 10g.The mass of ice is 50g. What is the final temperature of the mixture?

I know the conversion of steam to water is Ms(2.26x10^6J/kg)
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The solution calculates the final temperature of a mixture of steam and ice.

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Heat is absorbed by the ice and given up by steam
Let the final temperature of the mixture be t degrees celsius

1) Heat absorbed by ice:
mass of ice= 50 g= 0.05 Kg
specific latent heat of fusion of ice = 334 kJ.kg-1 334000 J.kg-1

Heat taken up for converting ice at 0ºC to water at 0ºC
= ...

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