Determine the mass of the remaining ice in the jar.A jar of tea is placed in sunlight until it reaches an equilibrium temperature of 32°C. In an attempt to cool the liquid, which has a mass of 170...

Determine the mass of the remaining ice in the jar.

A jar of tea is placed in sunlight until it reaches an equilibrium temperature of 32°C. In an attempt to cool the liquid, which has a mass of 170 g, 138 g of ice at 0°C is added. At the time at which the temperature of the tea (and melted ice) is 21°C.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A jar of tea is placed in sunlight until it reaches an equilibrium temperature of 32 C. In an attempt to cool the liquid, which has a mass of 170 g, 138 g of ice at 0 C is added. At the time at which the temperature of the tea (and melted ice) is 21 C, the mass of ice remaining has to be determined.

The mass of ice remaining at the end has to be less that 138 g.

The heat capacity of water and tea is assumed to be the same. The problem also requires the use of the enthalpy of fusion of ice which is 334 J/g.

Let the mass of ice remaining in the jar be M. The mass that has melted is equal to 138 - M. To melt the ice and raise its temperature to 21 C, the heat absorbed by the ice is equal to (138 - M)*334+21*4.186

The equilibrium temperature is 21 C. The heat given off by the initial liquid at 32 C while it cools to 21 C is (32 - 21)*4.186*170 = 7827.8 J.

At equilibrium (138 - M)*334+21*4.186 = 7827.8

=> (138 - M)*334 = 7827.8 - 87.906

=> 138 - M = 23.17

=> M = 114.82 g

At the moment when the temperature of the mixture is 21 C, 114.82 g of ice is left in the container.

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