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 200ml of Sumatran coffee at precisely 60.0°C. You then need to add enough milk at 3.00°C to drop the temperature of the coffee, initially at 80.0°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).

How will you prepare the beverage?

How much milk will you add?

Answer 1

the amount of coffee = 200 ml

the heat gain by the milk = the heat loss by coffee

X x 4.184 x ( 60 - 3 ) = 200 x 4.184 x ( 80 - 60 )

X x 4.184 x 57 = 200 x 4.184 x 20

X = 200 x 4.184 x 20 / 4.184 x 57

= 200 x 20 / 57

X = 70.175 g or 70.175 ml

so milk should add is 70.175 ml