Reference no: EM13808122

Newton's Law of Cooling:

The topic for the project is Newton's Law of Cooling, although you may choose a different title. The aim is to research how the temperature of a hot object is lost when it is kept in a cooler environment. You will need to use your mathematical skills, such as linear regression and knowledge of exponential functions. You will also be designing an experiment to find how water cools down from its boiling temperature.

The project is also a good introduction on how to write a professional report which you will be faced with in your career. You should take care to ensure that all spelling and punctuation is correct and that the overall look of the report is polished and clean.

The report should consist of the following components:

Introduction to the topic. Research the topic of Newton's Law of Cooling. Write the mathematical form of the law and explain its physical meaning. Try to justify the law using common sense and examples from all around you. Does Newton's Law of Cooling apply to convection, radiation, etc.? Briefly explain how, using Newton's Law of cooling, you may write the temperature of a cooling body as an exponential function of time. Is Newton's Law of Cooling still widely accepted? Are there any substitutes?

Description of the problem. Explain in detail how you would like to measure the rate of loss of temperature of water using an experimental set up. The experiment should be used to gather data for the temperature water versus time, as it cools down from its boiling point. Your descriptions and diagrams should be clear enough that someone new to the subject would be able to read your paper. One good measure of completeness is to ask yourself if you would be able to understand the equation by reading your description and studying your diagram. In other words your description should be a clear, self-contained exposition of the topic, much like one that you could find in the textbook on a given topic.

Description of the steps involved in solving the problem. Give a detailed description of the experiment and collecting the data. Mention that at least 15 data points should be collected on almost equal time intervals before the water reaches the environment temperature.

A detailed solution. Make a table of all of data you have gathered. Plot these data. What kind of function do you expect to see? Explain how using linear regression you can find the rate of loss of temperature for water. Apply this method, using Excel or other software, to your data and evaluate the numerical value of the rate of loss of temperature. Once done with that, write down the equation for the temperature of water versus time. Plot this equation and all of the data points on the same graph, and comment on the discrepancies you observe.

Conclusion and analysis of the results. Write a conclusion that highlights the major points of interest in your project and ties together some of the most interesting points you have covered.