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 by a device that will cool your coffee without dilution: a 200 g aluminum cylinder that you take from your freezer and place in a mug of hot coffee. If the cylinder is cooled to -20 degrees Celsius and then dropped into a large cup of coffee (essentially water, with a mass of 500 g) at 85 degrees Celsius, what is the final temperature of the coffee? 76.7 degrees 349.8 degrees 33.5 degrees 306.6 degrees

Explanation / Answer

In order to answer this question you need to know the specific heat of aluminum and water.
The source below says 0.900 J/g K and 4.186 J/g K respectively.

Let T be the final temperature to be found:
(0.900 J/g K) x (200 g) x (T - (-20))K = (180 T + 3600) 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:
180T + 3600 = 177905 - 2093T

2273 (T) = 174305
Solve for T algebraically:
T = 76.68 °C (or)

T = 76.7°C

hence the ans is (A)

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