A block of ice mass 200 gm is in a copper cup of mass 800 gm. Both the block of

Question

A block of ice mass 200 gm is in a copper cup of mass 800 gm. Both the block of ice and the cup are at 273 degree K. Water (mass 300 gm) at 100 degree C is now poured into the cup. What is the temperature of the mixture after equilibrium is reached. The Latent Heat of Vaporization for water is 2256 KJ/kg, the Latent Heat of Fusion for water is 333 KJ/kg, Specific Heat for water is 4180 J/kg K and the Specific Heat for copper is 386 J/kg K.

Explanation / Answer

Let final temperature = T Heat lost by water = 0.3 * (100-T) * 4180 = 125400 - (1254)T Heat gained by Ice = 0.2*333000 + 0.2*4180*(T-0) = 66600 + (836)T Heat gained by the cup = 0.8*386*(T-0) = (308.8)T Total heat lost = Total heat gained => T(1254+836+308.8) = 125400 - 66600 so, T = 58800/2398.8 = 24.51 degrees = Final temperature of the mixture.

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