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 230 g aluminum cylinder that you take from your freezer and place in a mug of hot coffee.

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

Express your answer using two significant figures.

Answer 1

specific heat of aluminium and water are, respectively,  0.900 J/g K and 4.186 J/g K.

0.900 J/g K x 230 g x (T + 20) ------------ (1)
4.186 J/g K x 500 g x (85 - T) ------------ (2)

equating (1) and (2), we get

207T + 4140 = 177905 - 2093T

solve for T, we get

2300 T = 173765

T = 75.55 K

or

T =76 K