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 65.0°C. You then need to add enough milk at 5.00°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 °C).

Answer 1

& Initial temperature of milk is s. escorkich in learer than temperature (800°c) of coffee Herre milk all gain heat & coffee aill release the heat Sumatral here, total volume of coffee ordered 250m which has bs.0.c. Let volume of milk added am volume of hot coffee (250e hart density of milk is igem as well an density of coffee in i gume war of milk added=&hx g & man of coffee - (250) 1 x 1g - (250-4) wow heat gained by milk (Irie mish & Chik (T- Ti) here, mmik man of milk an 9 Cmist - heat capacity of milk = 4.184 1/ge. – Finas temperature - 65.3.C. T. Initial temperature= 5.80 C I mitt = ax 4.184 x (65-5) I - 25600a

Similarly heat released by hot coffee Zoof - Mof x Coof & (Ti – 7) where, mof - man of coffee- & ore) Coof - heat copacity of coffee - 4.1845g. Tir Initiat Temp – 20.6. The Final Cup – 65.c. in Zof- (250-x) x 4.184 x (80-65)] = 0 2.76 (250-a) = 3,138 – 62.760. Now, It carilibrium milk - Zeof = 251.000 - 338–62.762 = (251.04 Gr. 76x) - 3138 313.99 = 3/38 in – 3120 10- so die aalom Amount of milk need to be adsed. - 10m