Newton's Law of Cooling - Investigating Exponential Functions
Lab Activity: We will perform an analysis of Newton's Law of Cooling by taking temperatures of Mr. S's coffee over 5 minute time intervals. First, note the room temperature. You will record the data, and then analyze the data in a variety of manners. You can access our class data from this link
(a) Create a computer generated scatter plot of the experimental data using WINPLOT, WINSTAT, EXCEL, or any other software with which you are familiar.
(b) Algebraically, determine an equation for the "curve of best fit" (HINT: common ratios and geometric sequences - works well if the time differences are constant)
Graph the points using WINPLOT (or a GDC) and then graph the function y = e x. Using your knowledge of transformations, apply and chronicle your various transformations of y = ex that resulted in superimposing this exponential function onto the data.
Follow this link to review plotting with WINPLOT
(d) Graph the data on semi-log paper (NOTE: make an adjustment in the data first!!!). Determine the equation of the line of best fit. Rearrange this equation to an exponential equation in base e. Show work. You can get two or three cycle semi-log paper by following this link
(e) Graph the data using technology (WINSTAT or GC) and determine the exponential regression equation of best fit (NOTE: make an adjustment in the data first!!!). Determine the coefficient of determination/correlation. Print the graph. What is the exponential equation that best fits the experimental data?
Follow this link to review plotting with WINSTAT
2. Now, you will check various sources to come up with the equation for Newton's Law of Cooling. State the law, interpret it, and define the variables used. Now compare your 4 equations from your analysis to the stated equation. Write a summary, conclusion, comment on various limitations in our analysis methods. As you write your summary, think about scoring well in the rubric .... communication, mathematical process: searching for patterns, and results: generalization.
3. Now use the Law to answer the question below.
(i) My Hot Chocolate is Too Hot!
You have just poured yourself a nice mug of hot chocolate. As you lift up the mug to take a sip, you realize the hot chocolate is too hot. You don't want to burn your tongue, so you decide to wait.
You walk over to the thermometer on the wall and note that the room temperature is 70 degrees. You assume that the temperature of the hot chocolate is about 200 degrees, because you added water that was almost boiling to the mug. You would like to wait until the hot chocolate is about 150 degrees. You use a thermometer to measure the temperature of the hot chocolate. After 2 minutes of cooling, it is at 190 degrees.
To the nearest minute, how much longer will you need to wait?