A 34.1g cube of ice, initially at -20C, is dropped into a cup of water that is a

Question

A 34.1g cube of ice, initially at -20C, is dropped into a cup of water that is at 0.00C. As heat flows from the water to the ice, water freezes to the ice cube until ice cube reaches a temperature of 0.00C. What is the mass of water that froze in this process?

Hint Let Qhot be the heat that flows from the water. The water is already at its freezing temperature, so only freezing occurs and Chot mL, where m is the mass of water that freezes Let Qcold be the heat that flows into the ice. The temperature of the ice increases,so QcoldmcAT, increases, so Qcold m'dAT. where m' is the mass of the ice cube and c is the specific heat of the ice.

Explanation / Answer

mass of ice mi = 34.1 g = 0.0341 kg, temperature of ice T1 = -20 0C = 253.15 k

mass of water mw = ?, temperature of water is 0 0C = 273.15 k

when ice dropped in to cup of water heat flows from water to ice so that water looses heat energy an ice gains equal amount of heat enery

so that water freezes and ice cube have temperature of 0 0C = 273.15 k = common temperatur

heat gain by ice cubes is D = m c delta T = 0.0341*2.03(273.15 - 253.15) =1.3844 J

now heat lost by water is Q = m*Lf = => 1.3844 = m *334 ==> m = 0.00414 kg

so mass of water that froze in the process is 0.00414 kg

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