Question

How many mL of cream at 5 degrees with a density of 1.35g/ml must be mixed...

How many mL of cream at 5 degrees with a density of 1.35g/ml must be mixed with 180ml of coffee at 95degrees so that the resulting combinations will have a temperature of 80degres? the specific heat of cream is 3.25j/g C. assume the density of water is 1g/ml

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Answer #1

CONCEPT: The problem can be solved by using the following equation

heat gained by ice cream = - Heat lost by coffee

- sign indicates heat is lost

SOLUTION:

Heat lost by coffee = - mass of coffee (Mc) X specific heat of coffee (Cc) X Temperature difference (ΔT)

Mc = Volume X density = 180mL X 1 = 180 g

Cc = specific heat of water = 4.2J/g

ΔT = Tfinal - Tinitial

Similarly heat gained by ice cream = Mi X Ci X ΔT

Ci = specific heat of ice cream

Mi = mass of ice cream = Volume of ice cream (Vi) / density

ΔT = Tfinal - Tinitial

(Vi / density) X Ci X ΔT = Mc X Cc X ΔT

(Vi / 1.35g/mL) X 3.25 J/g/oC X (80 oC- 5oC) = -[180 X 4.2 J/goC X (80oC - 95oC)]

Vi X 180.55 = 11340

Vi = 62.8 mL

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