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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 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 y C).
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

Respuesta :

Answer:

  • The amount of milk in ml you must add to reach 70.00ºC is 56.2 ml.

Explanation:

1. Change of temperature of the milk.

Milk will heat up from 1.00°C. Naming Qm the heat absorbed by milk, Mm the mass of milk added, in grams, and C the specific heat:

  • Qm = Mm × C × (70.00°C - 1.00°C)

2. Change of temperature of the coffe.

Coffe will cooldown from 90.0°C. Naming Qc the heat released by coffe, Mc the mass of coffe, in grams, and C the specific heat:

  • Qc = Mc × C × (90.0°C - 70.0°C)

3. Final mixture

The amount of coffe at 90.0°C plus the amount of milk at 1.00°C is 250 ml

Since the density is assumed to be 1.000g/ml, the mass is 250 g.

  • Mm = 250 g - Mc

4. Assumptions:

  • C = 4.184 J/gºC, for both milk and coffee
  • Qm = Qc, because the coffee in in an insulated travel mug.

5. Calculations:

  • Qm = Qc

  • Mm × C × (70.00°C - 1.00°C) = (250g - Mm) × C × (90.0°C - 70.0°C)

  • Mm × 69.00 = (250 - Mm) × 20.00

  • 69Mm = 5,000 - 20Mm

  • Mm = 5,000 / (89)

  • Mm = 56.2 g

Since the density is 1.000g/mol, 56.2g is 56.2 ml

Answer: 56.2 ml