The Cooling Coffee Conundrum · AI Generator #GEN-CDE66761

Physics · thermodynamics

Problem

A barista notices that when she pours hot coffee at temperature

T_h = 85°\text{C}

into two identical ceramic mugs in a room at

T_r = 20°\text{C}

, something interesting happens. She fills the first mug completely to the brim with

V_1 = 250\;\text{mL}

of coffee. The second mug she fills only halfway with

V_2 = 125\;\text{mL}

of the same coffee, leaving the top half of the mug empty but sealed (trapping air above the coffee). After

t = 5\;\text{minutes}

, she measures the temperature of both coffees and finds they have cooled to

T_1 = 73°\text{C}

and

T_2 = 68°\text{C}

respectively. Assuming Newton's law of cooling applies and that the ceramic mugs have identical thermal properties, what is the ratio of the effective surface areas through which heat is lost for the two configurations?

Related theory

thermodynamics

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