Physics : HEAT AND ENERGY?

2015-09-25 2:45 am

Mr Yip prepares a cup of cold drink by adding ice cubes into a cup of coffee initially at 40C. The mass of the coffee is 0.3 kg and the mass of an ice cube is 0.02 kg. Assuming that all ice cubes are completely melted, at least how many ice cubes have to be added to lower the temperature of the coffee to 10C? (The specific heat capacity of coffee is 4000Jkg^-1C^-1)

回答 (1)

micatkie

2015-09-25 3:56 am

✔ 最佳答案

Specific latent heat of ice = 334000 J/kg
Specific heat capacity of water = 4200 J/(kg °C)
Specific heat capacity of coffee = 4000 J/(kg °C)

Assume that n ice cubes have to be added.

Heat gain by the ice cubes
= (Heat gain for melting ice) + (Heat gain to rise temperature 0°C to 10°C)
= (0.02n kg) × (334000 J/kg) + (0.02n kg) × [4200 J/(kg °C)] × (10 °C)
= 7520n J

Heat loss by the coffee
= (0.3 kg) × [4000 J/(kg °C)] × (40 - 10 °C)
= 36000 J

Heat gain by the ice cubes = Heat loss by the coffee
7520n = 36000
n = 4.8

At least 5 ice cubes have to be added. ...... (Ans)

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