How much milk will I need in mL?

Question

During the summer after your first year at Carnegie Mellon, you are lucky enough to get a job making coffee at Starbucks, but you tell your parents and friends that you have secured a lucrative position as a "java engineer." An eccentric chemistry professor (not mentioning any names) stops in every day and orders 250ml of Sumatran coffee at precisely 75.0°C. You then need to add enough milk at 3.00°C to drop the temperature of the coffee, initially at 95.0°C, to the ordered temperature.

Calculate the amount of milk (in ml) you must add to reach this temperature. Show all your work in the provided spaces.

In order to simplify the calculations, you will start by assuming that milk and coffee have the specific heat and density as if water. In the following parts, you will remove these simplifications. Solve now this problem assuming the density is 1.000 g/ml for milk and coffee and their specific heat capacity is 4.184 J/(g ºC).

Hint: the coffee is in an insulated travel mug, so no heat escapes. To insulate a piece of glassware in Virtual Lab, Mac-users should command-click (or open-apple click) on the beaker or flask; Windows users should right click on the beaker or flask. From the menu that appears choose “Thermal Properties.” Check the box labeled “insulated from surroundings.” The temperature of the solution in that beaker or flask will remain constant.

Answer 1

Assume milk and coffee have the same density as water (1 g/ml) and the same specific heat as water (4.184 J/gº).

Heat lost by the 90º coffee must = heat gained by the 3.00º milk such that the final temperature = 75.0º

The coffee temp will go from 95º to 75º and the temp of the milk will go from 3º to 75º

heat lost by coffee = q = mC∆T = (250 g)(4.184 J/gº)(95 - 75º) = 20,920 J

This amount of heat must be that gained by the milk. Therefore...

heat gained by milk = q = mC∆T = 20,920 J = (x g)(4.184 J/gº)(75º - 3º) = 301.2 x

x = 69 mls of milk