The Cooling Coffee Paradox · AI Generator #GEN-2A4D14E6
Physics · thermodynamics
Problem
A barista notices something puzzling about coffee cooling. She prepares two identical cups of coffee, each containing m=250g of coffee initially at temperature T0=85°C. The room temperature is Tr=20°C.
To the first cup, she immediately adds mc=50g of cream at temperature Tc=5°C. To the second cup, she adds the same amount of cream, but waits exactly t=5minutes before adding it.
She discovers that both cups reach the same final temperature Tf after the cream is added and thermal equilibrium is established. Given that coffee loses heat to the environment following Newton's law of cooling with rate constant k=0.025min−1, what is the final temperature Tf of both cups?
Assume coffee and cream have the same specific heat capacity and density, and neglect any heat lost during the brief mixing process.