The Coffee Cooling Surprise · AI Generator #GEN-750D39F4
Physics · thermodynamics
Problem
A student conducts an experiment with two identical coffee mugs, each containing 250ml of coffee initially at 85°C. The first mug is left uncovered in a room at 20°C. The second mug has a thin layer of vegetable oil (density 0.92g/cm3, thickness 2.0mm) carefully poured on top to create a barrier that completely prevents evaporation while still allowing heat conduction.
After 10 minutes, the uncovered coffee has cooled to 65°C, while the oil-covered coffee has only cooled to 75°C. Assuming the dominant heat loss mechanism for uncovered coffee is evaporation (with negligible conduction/convection), and that the oil layer conducts heat at the same rate as the coffee surface would lose heat through conduction/convection alone:
What is the mass of water that evaporated from the uncovered mug during the 10-minute period?
Take the specific heat of coffee as c=4200J/(kg⋅°C), the latent heat of vaporization of water as Lv=2.26×106J/kg, and the density of coffee as 1.0g/cm3.