Dr. Sarah's Demo 4 on Newton's Law of Cooling.

Write down a reasonable differential equation which models the process of water in a freezer. Explain why your model is reasonable.

>

How would you solve this by hand if you had to?

What is a reasonable temperature for hot tap water? For cold tap water?

We would like to plot the solutions to the differential equation obtained with the different initial condition. First, using only one Maple command, dsolve your differential equation with the hot tap water initial condition, unapply it and call this solution "hotsolution". When you are done with this step, call me over and show this to me before moving on!

>

Now, using only one Maple command, dsolve your differential equation with the cold tap water initial condition, unapply it and call this solution "coldsolution".

>

We will display both solutions in different colors, so we will need with(plots):

> with(plots):

Plot the hotsolution with the color of the curve being red.

>

Set hotplot equal to the plot of a red hotsolution - be sure to use ":" instead of ";" at the end of this Maple command.

>

Set coldplot equal to the plot of a blue hotsolution.

>

Now we will display both plots:

> display({hotplot,coldplot});

Which takes less time to freeze? Why?

>

What are some errors one might encounter in a real life experiment? Could errors reverse the results?

Which freezes fastest? (ie which has the fastest rate of change)? Why?

Hit enter at the end of the next line:

The cafe-ole vs black coffee cooling experiment