Question #219632

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 70.0°C. You then need to add enough milk at 1.00°C to drop the temperature of the coffee, initially at 90.0°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).

Expert's answer

The coffee needs to give up heat to go from 80.0 C to 75.0 C. This heat is given by

"Qc = c x mc x \u0394t"

where c is the specific heat of the coffee, m is the mass (equal to volume), Δt the temperature change.

The added milk needs to absorb that amount of heat according

"Qm =mm x c x \u0394t"

As the densities and specific heats are assumed to be that of water,

Q_{c} = Q_{m} x m_{c} x Δt = Q_{m} =m_{m} x c x Δt

c x 75.0 mL x (80-75) = m_{m} x c x (75 - 1). As the c's are considered to be the same, they cancel out. Solve for m_{m} which will be the mL of milk to be added.

answer: 5.07 mL of milk.

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