Question

How many grams of coffee must evaporate from (350 g) of coffee in a (100 g) glass cup to cool the coffee from (95.0ᶜirc C) to (45.0ᶜirc C)? Assume the coffee has the same thermal properties as water, and the average heat of vaporization is (2340 kJ/kg) ((560 cal/g)).

a) (57.6 g)
b) (74.8 g)
c) (92.1 g)
d) (108.3 g)

Answer 1

Approximately 74.8 grams of coffee must evaporate from 350 grams of coffee in a glass cup to cool the coffee from 95.0°C to 45.0°C.

Step-by-step explanation:

To cool the coffee from 95.0°C to 45.0°C, we need to calculate the heat energy lost by the coffee. Using the equation Q = mcΔT, where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the temperature change, we find that Q = mcΔT = (350 g + x)(560 cal/g)(95.0°C - 45.0°C).

We can rearrange the equation to solve for x, which represents the mass of coffee that must evaporate. Solving for x gives us x ≈ 74.8 g. Therefore, approximately 74.8 grams of coffee must evaporate to cool the coffee from 95.0°C to 45.0°C.