Brewed coffee is often too hot to drink right away. You can cool it with an ice

Question

Brewed coffee is often too hot to drink right away. You can cool it with an ice cube, but this dilutes it. Or you can buy a device that will cool your coffee without dilution - a 220 g aluminum cylinder that you take from your freezer and place in a mug of hot coffee.

Part A

If the cylinder is cooled to -20C, a typical freezer temperature, and then dropped into a large cup of coffee (essentially water, with a mass of 500 g) at 85C, what is the final temperature of the coffee?

Brewed coffee is often too hot to drink right away. You can cool it with an ice cube, but this dilutes it. Or you can buy a device that will cool your coffee without dilution - a 220 g aluminum cylinder that you take from your freezer and place in a mug of hot coffee.

Part A

If the cylinder is cooled to -20C, a typical freezer temperature, and then dropped into a large cup of coffee (essentially water, with a mass of 500 g) at 85C, what is the final temperature of the coffee?

Explanation / Answer

specific heat of water is 4186 J/kgC
specific heat of Aluminum is 900 J/kgC
T is final temperature

heat stored in the Al is E = 900 J/kgC x 0.22 kg x (T–(–20))
Heat removed from water is E = 4186 J/kgC x 0.5 kg x (85–T)
set them equal and solve for T
900 x 0.22 x (T+20) = 4186 x 0.5 x (85–T)
198T + 3960 = 177905 – 2093T
173945 = 2291T
T = 75.93ºC

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