I\'m probably making this harder than it needs to be... Brewed coffee is often t
ID: 1705074 • Letter: I
Question
I'm probably making this harder than it needs to be...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 180 aluminum cylinder that you take from your freezer and place in a mug of hot coffee.
If the cylinder is cooled to -20, a typical freezer temperature, and then dropped into a large cup of coffee (essentially water, with a mass of 500 ) at 85, what is the final temperature of the coffee?
Explanation / Answer
In this problem, I'm assuming that aluminum should have a mass of 180 grams and the water a mass of 500 grams.
Use the formula mct.
Energy absorbed by Aluminum = Energy lost by Coffee
By this condition, the temperature of the entire system is the same throughout. Let x be the final temperature of the system.
(180)(.902)(x - (-20)) = (500)(4.184)(85 - x)
162.36x + 3247.2 = -2092x + 177820
2254.36x = 174572.8
x = 77.44
So the final temperature of the coffee is 77.44 degrees.