When Should I Drink My Hot Chocolate?
A cup of hot chocolate with an Arduino.Copyright 2015 Brian Palacios, SMARTER RET Program, School of Engineering, Polytechnic Institute of NYU
Students act as food science engineers as they explore and apply their understanding of cooling rate and specific heat capacity by completing two separate, but interconnected, tasks. In Part 1, student groups conduct an experiment to explore the cooling rate of a cup of hot chocolate. They collect and graph data to create a mathematical model that represents the cooling rate, and use an exponential decay regression to determine how long a person should wait to drink the cup of hot chocolate at an optimal temperature. In Part 2, students investigate the specific heat capacity of the hot chocolate. They determine how much energy is needed to heat the hot chocolate to an optimal temperature after it has cooled to room temperature. Two activity-guiding worksheets are included.
The concepts of heat exchange and cooling rates are applicable to a wide range of engineering fields including heating and cooling systems, microprocessors, internal combustion engines, and food industry engineering, to name a few. For example, knowledge of the heat capacity and cooling rates of chocolate is required for engineers to design production machinery and storage equipment—as well as to determine processing times—for the manufacture of chocolate. Because food's physical properties and conditions vary greatly, engineers also make mathematical models for food properties in order to predict the effects of changing chemical composition and temperature on food. Acting as engineers, students apply math skills, an understanding of the concepts of cooling rates and heat capacity, and technological tools to cups of hot chocolate as they determine the time to reach optimal drinking temperature and the energy needed to heat the liquid beverage to an optimal temperature.
After this activity, students should be able to:
- Explain the significance of exponential decay and how it relates to cooling liquids.
- Determine a mathematical model for a real-world scenario involving exponential decay.
- Calculate the specific heat capacity of a liquid.
- Determine the amount of energy required to heat a liquid to a particular temperature.