Question

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

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 (M_{c}) X
specific heat of coffee (C_{c}) X Temperature difference
(ΔT)

M_{c} = Volume X density = 180mL X 1 = 180 g

C_{c} = specific heat of water = 4.2J/g

ΔT = T_{final} - T_{initial}

Similarly heat gained by ice cream = M_{i} X
C_{i} X ΔT

C_{i} = specific heat of ice cream

M_{i} = mass of ice cream = Volume of ice cream
(V_{i}) / density

ΔT = T_{final} - T_{initial}

(V_{i} / density) X C_{i} X ΔT = M_{c} X
C_{c} X ΔT

(V_{i} / 1.35g/mL) X 3.25 J/g/^{o}C X (80
^{o}C- 5^{o}C) = -[180 X 4.2 J/g^{o}C X
(80^{o}C - 95^{o}C)]

V_{i} X 180.55 = 11340

**V _{i} = 62.8 mL**

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