Experiment and mathematical model for the heat transfer in water around 4 °C

• Published in: European journal of physics Vol. 38; no. 2; pp. 25102 - 25114
• Main Authors: Ogawa, Naohisa, Kaneko, Fumitoshi
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.03.2017
• Subjects: 4 degrees Celsius; convection; heat diffusion; water
• ISSN: 0143-0807; 1361-6404
• DOI: 10.1088/1361-6404/38/2/025102

Water, which is the habitat for a variety of living creatures, has a maximum density at 4.0 °C. This crucial property is considered to play a very important role in the biology of a lake and also has a close relationship with the areas of environmentology and geoscience. It would be desirable for students to confirm this important property of water themselves by carrying out simple experiments. However, it is not easy to detect the maximum density at 4.0 °C because the temperature dependence of the water density is very small close to its freezing point. For example, the density of water is 0.999 975 g cm−3 at 4.0 °C and 0.999 850 g cm−3 at 0.1 °C. The aim in this manuscript is to demonstrate a simple experiment to detect 4.0 °C as the temperature of maximum density, in which the time dependence of the water temperature is measured at several different depths by chilling the water surface. This is a simple experiment that can also be performed by high school students. We also present a mathematical model that can explain the results of this experiment.