The Cooling Coffee Puzzle · AI Generator #GEN-250C8E6D
Physics · thermodynamics
Problem
A barista notices that when she makes two identical cups of coffee at , but serves them in different cup materials, they cool at noticeably different rates. The ceramic cup has thermal mass while the glass cup has thermal mass . Each cup contains of coffee (thermal mass ). Both cups lose heat to the environment at a rate proportional to their temperature difference from the environment, with the same proportionality constant for both cup-coffee systems. After exactly (5 minutes), what is the temperature difference between the coffee in the two cups? Take the specific heat of coffee to be the same as water: .Intuitive explanation
Newton's cooling law tells us that systems with different thermal masses cool at different rates—the key is recognizing that the cup material acts as a thermal buffer. A ceramic cup, with its larger heat capacity, absorbs more energy from the coffee initially, slowing its temperature drop; the glass cup absorbs less, so the coffee cools faster. Both systems follow exponential decay toward room temperature, but their different total thermal masses () mean they reach different temperatures after the same elapsed time. You'll need to apply the exponential cooling formula separately to each system and compare.
Intuitive explanation
Newton's cooling law tells us that systems with different thermal masses cool at different rates—the key is recognizing that the cup material acts as a thermal buffer. A ceramic cup, with its larger heat capacity, absorbs more energy from the coffee initially, slowing its temperature drop; the glass cup absorbs less, so the coffee cools faster. Both systems follow exponential decay toward room temperature, but their different total thermal masses () mean they reach different temperatures after the same elapsed time. You'll need to apply the exponential cooling formula separately to each system and compare.