The Cooling Coffee Mystery · AI Generator #GEN-F398652C
Physics · thermodynamics
Problem
A physics student notices something puzzling about her morning coffee routine. She always pours coffee at 85°C into two identical ceramic mugs and adds the same amount of cold milk at 4°C. However, she adds milk to the first mug immediately, while she waits exactly 3 minutes before adding milk to the second mug. Both mugs then sit for an additional 5 minutes before she drinks from them.
Surprisingly, she finds that both mugs end up at nearly the same final temperature of 52°C, despite the different timing of milk addition. The room temperature is 22°C.
Given that the heat capacity of coffee is essentially that of water (4.18×103J/(kg⋅K)), the density of both liquids is 1000kg/m3, and Newton's law of cooling applies with the same cooling coefficient for both scenarios, determine the volume of milk added to each mug. Assume the total volume in each mug is 250mL after adding milk.