Grade 12:Coffee and Milk
You buy a large coffee (300 ml) at 80 degrees and four milks (15 ml each) at 4 degrees, and get into your car which stays at a constant temperature of 16 degrees. It will be a 10 minute drive before you can drink the coffee, and you want it to be as hot as possible at that time. Do you put the milk into the coffee mug at the beginning or after the 10 minutes when you’re ready to drink it? Do you mix first and then drive or drive first and then mix?
Mix last. We are given the resulting temperatures if the two liquids are kept separate. Our problems then is to solve the mixing principle.
Mix first. The previous case gives us the idea we need to find the temperature if we mix right away. It remains to capture the mechanism that describes how temperature difference leads to temperature change. This is a significant example of exponential decay.