You are a producer of artisan ice-cream. In the ice cream making process, you ad

Question

You are a producer of artisan ice-cream. In the ice cream making process, you add cubes of frozen milk to the ice cream batter to rapidly cool the custard based batter the instant it reaches the setting point. The ice cream batter has a temperature of 98 °C and a specific heat capacity of 3.68 kJ/(Kg× °C). The frozen milk cubes have a temperature of -18 °C and a specific heat capacity of 1.88 kJ/(kg×°C). The latent heat of fusion for frozen milk is 331 kJ/kg. The specific heat capacity for liquid milk is 4.07 kJ/(Kg× °C).

a. How much heat, Q, must be lost from 15 kg of ice cream batter in order to cool it to 50°C? (1 pt)

b. How much heat does it require to melt 5 kg of frozen milk cubes? (1 pt)?

c. How large a mass of frozen milk cubes must you add to cool 15 kg of ice cream batter from 98°C to 50°C? (Hint: The total amount of heat energy must remain constant, so the heat gained by one system must equal the heat lost by the other system. Remember that the final temperature of the melted milk must also be 50°C) (3 pt)

Explanation / Answer

a) Q = m c deltaT

Q = 15 x 3.68 x (98 - 50) =2649.6 kJ

b) Q = m c delatT + mL

Q = 5 x 1.88 x 18 + 5 x 331 = 1824.2 kJ

c) we take m kg of frozen milk .

so, 2649.6 = m x 1.88 x18 + m x331 + m x4.07 x 50

2649.6 =568.34m

m = 4.66 kg

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