Coffee Problem
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First watch the Introductory Video and Support Information on the upper left corner to learn how to use this simulation.
Then solve the following problem.
During the summer after your first year in college, 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 65.0°C. You then need to add enough milk at 4.00°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.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.
Heat transferred q, can be calculated as q = m c DT, where m is the mass of matter, c is the specific heat capacity in J/(g ºC), DT is the temperature change (DT = final temperature – initial temperature).
Heat released by coffee can be expressed as:
q coffee=mcoffeeccoffeeDTcoffee,
where DTcoffee= 65oC – 95oC = -30oC
mcoffee= Vcoffeedcoffee
Heat absorbed by milk can be expressed as:
q milk=mmilkcmilkDTmilk ,
where DTmilk= 65oC – 4oC = 61oC
mmilk= Vmilkdmilk
Since the coffee mug is insulating, the overall heat transferred within the mug is zero. That is,
q coffee= – q milk.
Now we have: mcoffeeccoffeeDTcoffee = – q milk =mmilkcmilkDTmilk
Plug DTcoffee= -30oC, DTmilk= +61oC, mmilk= Vmilkdmilk, and mcoffee= Vcoffeedcoffee into the above equation we got: Vcoffeedcoffeeccoffee(-30oC) = – Vmilkdmilkcmilk(61oC)
Since we assume dcoffee = dmilk = 1.000 g/mL and ccoffee = cmilk = 4.184 J/(g ºC), we can divide both sides of the above equation by -ccoffeedcoffee ( or -dmilkcmilk) to simplify the equation as: Vcoffee(30oC) = Vmilk(61oC)
Since the ordered coffee has a total volume of 200 mL, we can express Vcoffee as:
Vcoffee = 200 – Vmilk
Plug Vcoffee = 200 – Vmilk into Vcoffee(30oC) =Vmilk(61oC), we got
(200 – Vmilk) (30oC) = Vmilk(61oC)
Solve the above equation for Vmilkand caluateVcoffee. Show your work on Data Sheet.
(200 – Vmilk) (30oC) = Vmilk(61oC)
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