Mixing Water for the Training Room Foot Tub

The Foot Tub Puzzle

1After long track practices, the athletic trainer at Lakeview Middle School, Ms. Odalys Ferreira, fills a foot tub with water from a warm tap and a cool tap for runners with sore feet. Team manager Kenji Valdés noticed that some tubs came out too hot and others too cool, even though she used the same two taps. He wondered what decides the final temperature when two samples are mixed.

2Kenji set up an investigation in the training room. He used foam cups with lids so that little energy would escape into the room. In each trial he put cool water at 10 °C into a cup, measuring its mass on a scale. Then he poured in a measured mass of warm water from a tap set to 50 °C, closed the lid, stirred gently and recorded the temperature once it stopped changing. For Trial 5, Ms. Ferreira heated the warm water to 70 °C and poured it in herself. He kept the cups, the lids, the stirring and the room the same in every trial. He changed the mass of each sample, the starting temperature of the warm sample and, in one trial, the type of matter.

3For Trial 6, Kenji wanted to compare water with a different type of matter. He used 100 g of small glass marbles warmed to 50 °C in a bath of warm water. Ms. Ferreira lifted them out with a slotted spoon, patted them dry and tipped them into the cool water. Kenji ran every trial three times, and the table shows the averages.