A 41 g ice cube at 0.0°C is added to110 g of water in a 62 g iron cup. The cup a

Question

A 41 g ice cube at 0.0°C is added to110 g of water in a 62 g iron cup. The cup and the water have aninitial temperature of 45°C. (a) Find the equilibrium temperature of the cupand its contents.
   ________?°C (b) Suppose the iron cup is replaced withone of equal mass made from silver. Is theequilibrium temperature with the silvercup greater than or less than the iron cup?
__________?
(a) Find the equilibrium temperature of the cupand its contents.
   ________?°C (b) Suppose the iron cup is replaced withone of equal mass made from silver. Is theequilibrium temperature with the silvercup greater than or less than the iron cup?
__________?

Explanation / Answer

mass of ice m = 41 g mass of water M = 110 g mass of iron cup M ' = 62 g Initial temperature of cup and water t = 45 oC Initial temp of ice t ' = 0 oC Heat lost by iron anf water = heat gain by ice M ' C ' dt + M C dt = m L + m C dt ' where C ' = specific heat of iron = 0.1072 cal /goC          dt = 45-T           C =specific heat of water = 1 cal / g oC           dt ' =T - 0 = T           L =latent heat of fusion of water = 80 cal / g substitue values we get , 6.65 (45-T ) + 110 ( 45-T ) = 3280 + 41 T from this final temp T = 12.49 oC

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