Heat and Phase Change: Latent Heat

Question

A thermos contains 160 cm3 of coffee at 85°C. To cool the coffee, you drop two 15 g ice cubes into the thermos. The ice cubes are initially at 0°C and melt completely. What is the final temperature of the coffee?

Answer 1

specific heat of water is 4.186 kJ/kgC

heat of fusion of ice is 334 kJ/kg

density of water at 20C = 0.998 g/cm³ = 998 kg/m³

switching to metric

160 cm³ = 0.00016 m³

mass of water = 998 kg/m³ x 0.00016 m³ = 0.160 kg

ice 15g = 0.015 kg

Energy released on melting the ice:

E = 334 kJ/kg x 0.015 kg x 2 = 10 kJ

that energy is applied to heating the water

10 kJ = 4.186 kJ/kgC x 0.160 kg x T

T = 15 degrees C

which brings the water down from 85 to 70

but there is still the water from the ice, at 0C and it will also cool the total

That's a simple proportion

0.015 kg at 0C vs 0.160 kg at 70C

(15/160)*70 = 6.6C

so final temp is 70 - 6.6 = 63.4 C

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