Device development with a mathematical model to study heat capacity of liquids

A simple device for studying the heat capacity of water was constructed for classroom use. It consists of a water-filled closed container with an inserted heating rod and a thermometer. Initially, the water temperature increases linearly with time but later shows a deviation from the linear trend. To explain the result, the heating rate is assumed to be proportional to the difference between the temperature of the rod and that of water. The device can also be used to measure the specific heat capacity of other common liquids. This article demonstrates a simple equipment design together with an application of calculus in an introductory undergraduate physics laboratory. It presents an opportunity for project-based learning as well as problem solving with an emphasis on mathematical model development.