200 g of coffee at 9 0 ∘ C stands in a 2 5 ∘ C room, and 20 g of cream at 5 ∘ C (same specific heat) is to be added. With Newton's law of cooling the excess temperature of the contents falls by a

Question

200 g of coffee at 9 0 ∘ C stands in a 2 5 ∘ C room, and 20 g of cream at 5 ∘ C (same specific heat) is to be added. With Newton's law of cooling the excess temperature of the contents falls by a factor 0.8 in ten minutes. By how many ∘ C is the coffee warmer after ten minutes if the cream is added at once rather than at the end (two decimals)?

TestHub · Accepted Answer

Use the excess over room temperature. Coffee: 65 , cream: − 20 . Cream first: 0.8 × 220 200 × 65 − 20 × 20 ​ = 45.82 . Cream last: 220 0.8 × 200 × 65 − 20 × 20 ​ = 45.45 . Difference = 0.36 ∘ C, so adding the cream at once is slightly better.

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