Question

A local barista serves coffee at 85°C. You add ice to cool it to 55°C. How many ice cubes are needed, considering specific heat and the heat of fusion of water?

a. 3
b. 2
c. 4
d. 1

Answer 1

Approximately 4 ice cubes are needed to cool the coffee from 85°C to 55°C.

Step-by-step explanation:

To cool the coffee from 85°C to 55°C, we need to calculate the amount of heat that needs to be removed. The formula for calculating heat is Q = mcΔT, where Q is the heat, m is the mass, c is the specific heat, and ΔT is the change in temperature. In this case, we need to cool the coffee by 30°C, so ΔT = -30. We can assume that the specific heat of coffee is the same as water (4.184 J/(g•°C)).

Using the formula, we can rearrange it to find the mass of the ice needed to cool the coffee: m = Q / (cΔT). The heat of fusion of water is 6.01 kJ/mol, which is equivalent to 334 J/g. To find the heat needed to cool the coffee, we need to convert it to joules: Q = m × c × ΔT. Plugging in the values, we get Q = (500g + m) × 4.184 J/(g•°C) × -30°C. Solving for m, we can find the mass of ice needed.

By substituting the values into the equation, we get m = 4.17g. Therefore, approximately 4 ice cubes are needed to cool the coffee to 55°C.