The Cooling Coffee Mystery · AI Generator #GEN-7B51A881
Physics · thermodynamics
Problem
A barista notices that when she pours hot coffee into two identical ceramic mugs at room temperature, something puzzling happens. The first mug is filled completely with 250mL of coffee at 85°C. The second mug is filled with only 125mL of the same coffee at 85°C, leaving the mug half-empty with air space above the coffee.
After 5 minutes, she measures the temperatures and finds that the half-filled mug has cooled to 71°C, while the completely filled mug has only cooled to 76°C. Both mugs were sitting in the same room at 22°C with no air circulation.
Assuming Newton's law of cooling applies (dtdT=−k(T−Tambient)) and that the cooling is dominated by heat transfer through the ceramic walls, determine the ratio of the effective thermal conductance of the half-filled mug to that of the completely filled mug.
Note: The thermal conductance k in Newton's law includes both the thermal properties of the mug and the heat transfer mechanisms present.