# Who Drinks Hotter Coffee?

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## Problem

Pinky and Perky both order coffee, and receive cups of it at the same temperature at the same time.

Pinky adds a small quantity of cool milk immediately, but does not drink his coffee immediately.

Perky waits some time before adding exactly the same quantity of milk of the same temperature as that which Pinky added.

Both Pinky and Perky then drink their coffee at the same time.

Who drinks the hotter coffee?

## Solution

By Newton's Law of Cooling, Perky's coffee loses heat faster than Pinky's.

When Perky adds his milk, it will have lost more heat to its surroundings than Pinky's.

Hence, after Perky has added his milk, Pinky's coffee will be hotter than Perky's coffee.

$\blacksquare$

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 1$: Miscellaneous Problems for Chapter $1$: Problem $15$