Question

During the summer, you have a job making coffee at starbucks, and you tell your friends and family that you have secured a position as a "java engineer. An eccentric chemistry professor stops in every day and orders 250mL of the house coffee at precisely 95 degrees C. THey then add enough milk (held at 4 degrees C) to drop the temperature of the coffee to 90 degrees C. Assume the density of coffee and milk are both 1.000 g/mL, and the specific heat of both is 4.186 J/g C

Calculate the mass of milk of added to the coffee.

Answer 1

The mass of milk is 14.5 grams

Step-by-step explanation:

Step 1: Data given

Volume of coffee = 250 mL = 0.250 L

Temperature of the coffee = 95.0 °C

Temperature of milk = 4.0 °C

Final temperature of coffee+ milk = 90.0 °C

Density of milk and coffee = 1.000 g/mL

Specific heat of milk and coffee = 4.186 J/g°C

Step 2: Calculate mass of coffee

Mass of coffee = 1.000 g/mL * 250 mL

Mass of coffee = 250 grams

Step 3: Calculate mass of milk

Heat gained = heat lost

Qmilk = - Qcoffee

Q = m*c*ΔT

m(milk)* c(milk) * ΔT(milk) = - m(coffee)*c(coffee)*ΔT(coffee)

⇒m(milk) = the mass of milk = TO BE DETERMINED

⇒c(milk) = the specific heat of milk = 4.186 J/g°C

⇒ΔT(milk) = the change of temperature of milk = 90.0 °C - 4.0 °C = 86.0 °C

⇒m(coffee) = the mass of coffee = 250 grams

⇒c(coffee) = the specific heat of coffee = 4.186 J/g°C

⇒with ΔT(coffee) = the change in temperautre of coffee = 90.0 °C - 95.0 °C = -5.0 °C

m(milk) * 4.186*86.0 = -250 * 4.186 * -5.0

m(milk) * 86.0 = -250*-5.0

m(milk) = 14.5 grams

The mass of milk is 14.5 grams