Aluminum Coffee Mugs

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 170g aluminum cylinder that you take from your freezer and place in a mug of hot coffee.If the cylinder is cooled to -20 `C, a typical freezer temperature, and then dropped into a large cup of coffee (essentially water, with a mass of 500g) at 85`C, what is the final temperature of the coffee?

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 0.17 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 0.17 x (T+20) = 4186 x 0.5 x (85–T)
153T + 3060 = 177905 – 2093T
174845 = 2246T
T = 77.8ºC

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