Problem 12.51 - Enhanced - with Feedback Brewed coffee is often too hot to drink
ID: 1561957 • Letter: P
Question
Problem 12.51 - Enhanced - with Feedback
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 290 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?
Express your answer using two significant figures.
Explanation / Answer
Let T be the final temperature to be found:
(0.900 J/g K) x (290 g) x (T - (-20))K = (261T + 5220) J gained by the Al
(4.186 J/g K) x (500 g) x (85 - T)K = (177905 - 2093T ) J lost by the coffee
Set the two expressions for heat gained/lost equal to each other:
261T + 5220 = 177905 - 2093T
Solve for T algebraically:
2353T = 172685
T = 73.38 °C