cooling project for students- answer key

Cooling of Liquids Project

Alexis Ploss, 5/7/15, High School Physics

Due Date: May 28th, 2015

You will be given three (3) weeks to explore, gather, and analyze your data. You will be expected to

submit your data and analysis in a written lab report format that you were provided at the beginning of

the semester. For each week you are late submitting your project, you will lose one (1) letter grade. No

reports will be accepted after June 11th, 2015 unless you have prior approval.

Objective:

The student will be able to demonstrate understanding of:

1. Basic Mathematica input

2. Exponential decay functions, and

3. The scientific method

4. Visual analysis of graphical outputs.

5. Modeling physical phenomena

The student will demonstrate this understanding through pre-analysis, collection of data, organization of

data, and post analysis in a written lab report format.

Printed by Wolfram Mathematica Student Edition

Grading Rubric:

Materials:

1. Raspberry Pi Model B+ or newer

2. Raspberry Pi Extension Board

3. Extension Board Ribbon (to connect your extension board to the Raspberry Pi). This is optional, but

will save you some time with setting up the circuit! If you’re not planning to use this, make sure

you see me because your required

4. Monitor with an HDMI hookup (could also use any TV with the same connection)

5. 10 MW resistor

6. A DS18B20 temperature sensor

7. Jumper wires

8. A glass, ceramic, and metal container

9. USB keyboard and mouse

10. Water, salt, vegetable oil (or another food-based oil), and milk

2 Cooling Project for Students.nb


Pre-Analysis:

1. Using the three (3) graphs below, analyze and draw conclusions about what the material of the

vessel is. On the line below each graph write either “C” for ceramic, “M” for metal, or “G” for glass.

Note: each letter should only be used once.

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____________C_______________ ____________G________________

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___________M________________

Cooling Project for Students.nb 3


2. Using the four (4) graphs below of liquids inside a glass container, analyze and draw conclusions

about what liquid each graph represents. On the line below each graph write either "W" for water, "SW"

for salt water, "VO" for vegetable oil, or "M" for milk

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____________SW______________ ____________VO_____________

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____________M________________ _____________W______________



Directions:

1. Setup your Raspberry Pi and Extension Board by following along with this dia-

gram.

2. Once you have the circuit set up correctly, you must test that the Raspberry Pi can detect the tempera-

ture sensor.

3. Type the following commands into the LX Terminal

è sudo modprobe w1-gpio

è sudo modprobe w1-therm

è cd /sys/bus/w1/devices

è ls

* At this point, you will see if the Raspberry Pi is detecting your temperature sensor and you

should see an output containing 28-XXXXXXXXXXXX. The X’s represent the ending digits and letters

that will be unique to your temperature sensor. From here, continue entering the provided code in the

LX Terminal.

è cd 28-XXXXXXXXXXXX

è cat w1_slave

*After entering this last line of code, the LX Terminal should output a two strings of data, and the

first line should end with “YES”. This is how you will know your temperature sensor is functioning

properly.

è cd

è sudo mathematica

4. Now that you’ve launched Mathematica as a superuser, you can begin to craft your program based

on the following code:



1. Setup your Raspberry Pi and Extension Board by following along with this dia-

gram.

2. Once you have the circuit set up correctly, you must test that the Raspberry Pi can detect the tempera-

ture sensor.

3. Type the following commands into the LX Terminal

è sudo modprobe w1-gpio

è sudo modprobe w1-therm

è cd /sys/bus/w1/devices

è ls

* At this point, you will see if the Raspberry Pi is detecting your temperature sensor and you

should see an output containing 28-XXXXXXXXXXXX. The X’s represent the ending digits and letters

that will be unique to your temperature sensor. From here, continue entering the provided code in the

LX Terminal.

è cd 28-XXXXXXXXXXXX

è cat w1_slave

*After entering this last line of code, the LX Terminal should output a two strings of data, and the

first line should end with “YES”. This is how you will know your temperature sensor is functioning

properly.

è cd

è sudo mathematica

4. Now that you’ve launched Mathematica as a superuser, you can begin to craft your program based

on the following code:

Import["/sys/bus/w1/devices//28-XXXXXXXXXXXX/w1_slave"]

temp:=N[ToExpression[StringTake[Import["/sys/bus/w1/devices//28-

XXXXXXXXXXXX/w1_slave"], -5]]/1000]

temp

*Using the command temp will allow you to take the temperature of the room and also used as

a check that the probe is reading realistic temperatures. Make sure you run the "temp" command

before each trial! You will need this data when developing the mathematical model!

wig = Association[ ];

RunScheduledTask[wig[Length@wig+1]=temp,{60,60}]

5. Use this code for each sample you have. It is very important to create different variables for each

liquid and vessel combination! I used wig here for "Water in Glass" and changed them for every

trial. You are going to need to do the following combinations of liquids and vessels:

1. Water in ceramic

2. Water in glass

3. Water in metal

4. Salt water in ceramic

5. Salt water in glass

6. Salt water in metal

7. Vegetable oil in ceramic

8. Vegetable oil in glass

9. Vegetable oil in metal

10. Milk in ceramic

11. Milk in glass

12. Milk in metal

6. After each trial, you must analyze the data you have collected. In order to do that, you must print your

association as a list by using:

è wiglist=Values[wig]

7. Once you have your data in list format, you should create a graph using:

è ListLinePlot[wiglist, Joined->True, PlotRange->Automatic]]



Developing the Mathematical Model:

In order to develop our models, we have to start with a few assumptions. The first assumption is that

the liquid is starting out at a higher temperature than the ambient temperature. What external factors do

you think will effect the rate of cooling? Hint: one of the factors should be room temperature!

Using the function T(t) to represent the temperature of the liquid over time, and the parameter A for

ambient temperature, and k for the proportionality constant. Assuming the rate of change of the liquid’s

temperature is proportional to the difference between the current liquid temperature and its ambient

temperature, develop a model of the rate of cooling for your liquids. Hint: How are dT/dt and T(t)-A

related?

Once you have developed your model, you will use this as a base to develop your second model. For

the first model, leave all of your parameters as variables. For the second, you should define the parame-

ter A as the inital temperature you took before that trial.

Now you should evaluate your model using the DSolve command, as follows:

DSolve@ your relation of T'@tD and T@tD, T@tD, tD

After evaluating DSolve, you should have you equation to enter into the NonlinearModelFit function.

NonlinearModelFit@each data set, DSolve solution, 8A, k, t<, tD

Data Collection:

Here are some general tips and rules to follow when collecting your data.

1. Always be true to your data! Don’t delete or otherwise alter data to fit your projected model.

It’s okay to be wrong, or have errors. It’s normal and it’s SCIENCE!

2. Try to use approximately the same amount of liquid in each vessel for each trial.

3. Make sure your experiment station is heat-safe. It might also be helpful to make sure it’s not in a

place where your pets or siblings can knock it over or hurt themselves.

4. Always use protective wear (potholders, long sleeves, etc.) when handling hot liquids, especially the

vegetable oil and milk.

5. When making your salt water, make sure you use the same amount of salt per unit volume of liquid.

Since we’re testing how salinity impacts cooling, have one trial with more heavily-salted water may

cause your data to have unnecessary errors making it harder to interpret.

6. Try your best to make sure the room temperature is approximately the same; don’t turn on the A/C

for one run and have it off for the next.

7. Make sure you use the same vessel for each liquid. If you used a certain coffee mug for your ceramic

vessel -- stick with that same one for every ceramic trial.

8. When inserting the probe into your liquid, try to make sure it isn’t touching the sides or bottom of the

vessel. This could interfere with the data you report.



Post-Analysis:

1. Does your experimental data that you collected match your anticipated results? If not, explain how it

differs from what you originally thought.

è Must mention slope of line

è If results don’t match anticipated results, must explain why

2. What further observations can you gather about your experimental data? Are any of your lists of data

you computed related to one another in any way? If so, what are the similarities or differences?

è Must mention y-intecept

è Must mention slope

è Must see connection between either similar liquid or similar vessels

3. Based on your calculations, what relationship best describes what happened in your system?

Only one answer is necessary

è T(t)= A+Exp[-kt]

è dT/dt= -k [T(t)-A]

4. Knowing that the large k you have indicates a faster rate of cooling, make a new model with k as the

dependent variable. Hint: What is k proportional/inversely proportional to? (This question does not

count for points)

è Preferrably kµ1/C

è Will also accept kµ1/m

5. Using your answer for question 4, develop a new hypothesis for a new experiment. Note: It is okay

to be wrong when forming a hypothesis! (This question does not count for points)

è Control all other variables in experiment, but vary the volume of the liquid to explore the

relationship of heat capacity and k.



cooling project for students- answer key

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