Everyday Science: The Coffee Problem

Science is around us all the time.  But we knew that, right?  As you drink your morning coffee, consider this problem posed to my college calculus class years ago:

You have just poured yourself a hot cup of coffee and are about to add cream, cold from the refrigerator, when the telephone rings.  Should you pour the cream before or after you answer the phone?  

Simple, right?  Our class was tasked to write a differential equation to describe the problem.  My time-weakened and diaper-dulled brain couldn’t even begin to tackle the problem now, but it could prove an interesting discussion for your middle school through high school homeschoolers.  Call it an opening bell attention gainer.  It might need to be accompanied with an explanation of why you would answer the phone at all when the person calling could just as well text or e-mail and then the entire problem would be solved.  But pretend for arguments’ sake you did have to get the phone.

Some questions that might come up:  What is the temperature at which you prefer to drink the coffee?  How hot is the coffee and how cold is the cream?  How long will the phone conversation last?  Once the cream is poured, how long will the coffee take to reach a drinkable temperature?  What other factors might be present that would affect the cooling rate of the coffee?  Ambient temperature of the room?  Mass of the cup?  Composition of the cup?  On what surface is the cup sitting?  Which factors will be most important in considering how fast the coffee will cool?  Which factors will be least important?  What if the cream started at room temperature?  Would it help slow cooling to put the coffee cup in a smaller space?  Is there a ceiling fan on?  Are any of these questions red herrings?

Heat transfer is taking place between the coffee and the air, between the cream and the coffee, between the coffee-cream mixture and the cup, and between the cup and the counter.  These transfers of heat are happening at different rates based on initial temperature of each, the mass or volume of each, and the temperature differential.  These transfers of heat follow the Second Law of Thermodynamics in an attempt to reach thermal equilibrium.  The Second Law of Thermodynamics states that entropy always increases.  Entropy is a measure of the disorder of the thermodynamic system.  Disorder increasing, energy dispersing, becoming distributed amongst other elements of the system.  A hammer falls when you release it from shoulder height.  A ball rolls downhill when you release it at the top of the hill.  Coffee cools to room temperature.  Heat transfers from hot to cold, always, and never the other way around unless work is injected into the equation, such as the forced heat transfer that happens in your refrigerator coils.  Entropy always increases. (Lets save closed and open system discussions for that high school physics class)

Heat always moves from hot to cold.  The hotter the hot body and the cooler the cool body, the faster the transfer will occur.  If your coffee sat on the counter at room temperature, would any heat transfer be occurring?  No, because thermal equilibrium has already been attained.  This should shed some light on the question of when to add the cream.  When you add the cream, you are reducing the initial temperature of the coffee and bringing it closer to room temperature right out of the gate.  Know the answer yet?

The three basic forms of heat transfer are convection, conduction, and radiationConvection is transfer by means of fluid flow, remembering that a fluid can mean a liquid or a gas.  Conduction is transfer between atoms in contact with each other, remembering that this can be the top layer of molecules of coffee and the bottom layer of air molecules, or the first layer of the cup, and so out and so up and so forth..  Radiation is heat transfer by means of electromagnetic waves, in this case, the charged particles of the hot coffee producing thermal radiation.  For this problem, the question can be asked how each of these processes are occurring, and how fast they are occurring, but these are incidental to answering the initial question of whether or not to add the cream before answering the phone.

Once you are done with your coffee, and your roundtable discussion of how fast it has cooled, you can answer the question of when to add the cream, and then watch this old video from the California Institute of Sciences, which Dr. Ross must have seen back in the day before he taught that differential equations class.  Did you answer the problem correctly?

Comments { 2 }

Questions for Young Scientists to Ask

These are great starting points to work on the scientific method with your student.  For elementary students, these are great springboards from which to use the scientific method.   You can develop an experiment to go with each of these questions (and we will post them here in coming weeks).  Complete a worksheet like the ones included at the bottom of this post, and you have just begun your Science Notebook.   Have fun!

  1. At what temperature does water boil?   Freeze?
  2. How could you separate water and sand?
  3. Does a light bulb give off heat?
  4. Does aluminum foil keep in heat?
  5. Can the sun cook food?
  6. Does the soil get warm when the sun shines on it?
  7. How does the ice cream freeze?
  8. How many colors are there in light (sunlight)?
  9. How fast do seeds germinate?  Different kinds of seeds?  At different temperatures?
  10. Can you grow plants from parts of plants?
  11. Do plants need light?
  12. Where does the water go that watered the plants?
  13. What are the parts of a flower?
  14. Does pollution hurt plants?  (Acid rain)
  15. How does gravity work on a plant?
  16. What are the parts of a corn plant?
  17. Does carbon dioxide (CO2) help a plant to grow?

Comments Off on Questions for Young Scientists to Ask

Inventions, Creative Thinking, and Problem Solving

by Kathleen Julicher
Of the many ways that distinguish people from animals, creativity and the ability to invent is most obvious.  God, when He breathed life into Adam, also gave him intelligence and the desire to create.  While creativity is given in some measure to all people, some like artists, inventors, or authors may have a special gift.  In our homeschools, all of our children will show a spark of creativity.  Nurture that spark in your children by using some of the ideas and resources mentioned in this article.
Creativity is the ability to create something new, or to change something to improve it.  We usually think of creativity as having to do mainly with art, but there is a technical kind of creativity which produces inventions and allows the scientist to solve problems and to design experiments.  Technical creativity and artistic creativity use a similar style of thinking, creativity, but in different ways.  In this way, inventions, artistry, and compositions are all products of creativity.  In science, creativity is expressed by invention, problem solving skills, design of experiments, and thinking of explanations of events.  Since an artist and a scientist use creative thinking in different ways, a good problem solver may not be able to paint, just as an artist may not be able to design experiments.  An excellent mathematical problem solver may not be able to arrange a room or design a bridge.  Technical problem solving and creativity are both part of inventing.
There have been many famous inventors in the past whom you can study in your homeschool.  Among them are Edison, Marconi, Da Vinci, Curie, Kettering, Whitney, Carver, Tesla, Land, Babbage, Bell, and the Wright brothers.  What can we study about these inventors?  What similar characteristics did they have?  Curiosity must have been one.  Other similar traits might be: the desire to try something new, the persistence to overcome obstacles; an idea or concept, or maybe a dream; a willingness to take the time to work on a project.  Most inventors have an ability to think “outside the box”.  “The box” refers to common knowledge, or the usual way of doing something.  Discuss the things inventors have in common with your children.  Does your student have any of those characteristics?  Have you told him so?  How would you encourage those characteristics?  Below is a list of activities you can do at home to encourage or to train your young inventors.
Practicing Inventing

  • Let the child use tools (saw, drill, sewing machine, soldering iron, etc.) (safely, of course)
  • Let them have scraps to work on.
  • Compliment them on their projects.
  • Be surprised and pleased when they change something. Even if it is not the way you would have done it.
  • Let them make something without the instructions.
  • Let them make mistakes.
  • Teach them to learn from mistakes without being critical.
  • Let them change the instructions.

There are thousands of other inventors about whom little has written.  For example, we do not know who invented the stirrup, the metal plow, the needle, the iron, weaving, or the written word, so we cannot study the inventors, only the inventions.  In cases such as these, your student can draw the invention, decide how it would affect the way work was done and try to imagine how life must have been without the invention.  For example, stirrups were a terribly important invention and literally transformed Asia and parts of Europe.  In the fifth century, the hordes of Mongolia had stirrups while the peoples they conquered did not.  How must it have been to ride without them for your feet?  How did a soldier swing a saber or throw a javelin accurately and with power while on his horse without stirrups?  By studying the befores and afters of inventions, students can learn about changing and adapting things.
Conflict with traditional thinking
The problem with creative thinking is that it involves a change in the way we do things, or look at things.  A conservative person will have a certain set of recipes to be used on certain days and will resist learning any new recipe and a new or different technique.  This person will ask “When the way we cook dinner is perfectly fine, why change it?”  And so it is with schooling,  If the way we school is working, then why change that?  The natural instinct of most people is to leave well enough alone.  Homeschoolers, by nature are in conflict with traditional schooling, but we can still exhibit conservative, non-creative thinking.  This is exemplified by those who refuse to leave the textbook to do some project or field trip.  Those who wish to teach inventing or creativity, though, must leave the text behind and move at least part of the time into divergent thinking  There are three steps to the teaching of creativity: 
  1. allowing time to think up ideas
  2. allowing the children’s ideas to be different
  3. allowing them to put the ideas into action.   
By doing these things to practice creativity, you encourage it.  You must also model creativity if you expect your children to be inventive.
Practicing creative thinking and invention is easy.  First, set aside some time, perhaps two hours per week, for an activity.  Next, check out some of the activities suggested or some of the books from the resource list for ideas.  If you are doing a craft or an art problem then collect the materials to use.  In this way, your young inventors will have the necessary materials (plus a few unnecessary ones) to do their projects.
The most important thing is that the atmosphere must be conducive to creative thinking.  Do not interrupt brainstorming as this will stop the flow of thinking.  While brainstorming, do not be judgmental or point out the obvious flaws in their ideas.  To do so will inhibit the free flow of thought.  You may expect a product to be made; that is, a physical invention or creation.  It is reasonable to provide a deadline for the work, too, as this will help the children stay focused on the problem at hand.  You should control your own desire to help solve the problem as that is an inhibitor of the children’s creativity.  This may be difficult to do if the problem is especially interesting.  Your own work on the problem must be as collaborator not as an actor.  You should give your student an opportunity to explain the workings of the product.  Smiling is very important for parents, too.
Measuring Creativity
Paul Torrance developed a test which attempts to measure four components of creative ability: fluency, flexibility, originality, and elaboration, all related to the ability to think creatively.  Fluency is the ability to think of many ideas on one topic, whereas flexibility is the ability to use given figures in original ways while elaboration is tested by asking the student to put many details on a picture.  There are other tests which try to measure creativity and each approaches the goal differently.  At home, you can encourage fluency, flexibility, and elaboration by practicing the same skills.  For example, give your child a drawing of a box.  Ask him or her to draw something with lots of details using the box.  He might turn the box into a house, an office, a railroad car, an airplane, a dinosaur, or a hologram of a planet.  The many details of the drawing show elaboration.  Give your student a set of pages with boxes and within each box draw an “x”.  Ask him to draw something different in each box, using the “x” in the drawing.  The idea is to have him draw many different pictures.  Another time you might want him to think of unusual things to draw, uncommon things, out of the lines.  This would be an exercise in originality.  List making is another way to practice creative skills.  Ask your child to make a list of all of the blue things in the room.  He will probably start out with a list of blue colored things, but later, he may start adding things like a sad face, or blues music tapes, the number “3” which seems to be colored blue in his mind’s eye.  The longer the list the better.
In science, we normally think of inventions and problem solving when we think of creativity.  That is another great way to practice creative thinking.  An example of problem solving would be to attempt to answer the question: how could you make a structure made of popsicle sticks stable, so it would not move when pushed? Can you design a car which is drivable by a person without using legs?  Or, what could you use to provide light for reading if your electricity went out?  Invention really is very much like problem solving and you can use problem solving activities to train your children to think inventively.
Creative problem solving ideas:

  • Use these materials: five paper clips, tape, scissors, and a fifteen inch piece of string, and one or two of the following: paper plate, socks, shoelaces, pencils, feathers, hot glue gun and a nail.  
  • Give your students a list of possible projects, like the following:
    • Design a toy for a cat
    • Make a chair for a doll
    • Make a noise maker
    • Design a game
    • Make a tool which will keep a person cool
  • Give your students a time limit and watch what happens!

You never know when creativity and problem solving may be needed.  Years ago, when homeschooling at the beach, we heard yells for help.  A man was being electrocuted and could not release the pipe because his muscles were in spasm.  After explaining to the children that we needed something which did not carry electricity in order to break the circuit in which the man was trapped, everyone fanned out, looking, and quickly returned with items they had found.  One brought a rope, another a board, another a plastic jug, and so on.  The rope did the trick and the electrical connection was broken.  Later, after the ambulance took the man to the hospital, we went over what had happened, reinforcing the ideas of problem solving, creativity, calmness, and electrical safety.
Creative thinking is important to our lives, it comes from God, and should be encouraged in our homeschools.  We can do this by giving them time to create things, by encouraging them, and by being non-judgemental about their ideas.  Plan a weekly time for problem solving and creativity play and your children will grow in their ability to be creative and flexible.
The Art of Problem Solving: Volumes 1 and 2 by Sandor Lehoczky and Richard Rusczky  These two books are a systematic study of problem solving techniques in arithmetic and higher maths.  The authors go beyond mere techniques and teach mathematical reasoning and because of this, the student who works in these books will gain a much deeper feel for mathematics.  They are especially useful in contesting.  Solution sets, too.
Creative Thinking and Problem Solving for Young Learners by Karen S. Meador.  This book is for the youngest of school children, K-4, and the author says that the activities can be used for even younger children.  Starting out with a definition of creativity, the author lays a foundation for the teacher who wants to learn to think creatively, too, and not just use activity sheets according to directions.  The lessons detail different aspects of creative thinking and list ideas designed to teach them.  Literature resources are even used although this is primarily a thinking book.  An excellent resource for homeschool.
Inventions, Inventors and You by Dianne Draze.  A very practical book for busy parents who want to do inventions and inventors in homeschool, but just can’t bring it all together (or don’t have the time).  There are pages to copy and use which provide short lessons in creative thinking and invention.  The book includes fourteen lessons with directions for the teacher, ideas for warming up that creative thinking, reproducible worksheets, many individual projects, and patent activities, plus the answers.  Use this book to build a year of invention.  Grades 3-7. 
The Inventive Mind in Science: Creative Thinking Activities by Christine Ebert and Edward S. Ebert II.  After discussing creativity and creative thought, the authors go straight into activities you can use at home to encourage creative thinking.  The problem of the conceptual block is important for anyone working on developing his creativity, and the authors systematically cover methods to avoid blocks.  The book offers three types of inventing to be used in the classroom: discovery, Rube Goldberg, and practical.  Taking inventions across the disciplines, an invention festival, and patent studies are included in this useful book.  One important part of the book is the Invent! card game used for desktop inventing.
Minds On Science by Hilarie Davis and Anne Dudley.  The appropriate subtitle for this series of books is: Lessons to Link Science and Thinking Skills.  Scientific problem solving and techniques to do it are the subjects of this book.  A plan for solving problems is included, as are lists of possible topics for investigation.  Activities are included in which the students are asked to observe, record, measure, and even make line charts!  The books reviewed are for grades 1-3.  Use this set of books for a great way to integrate thinking and science.  Recommended  A volume each for grades 1-3.
Problems in Search of Creative Solutions by H. Allen Murphey  A wonderful book for your technically creative kids!  This is the book to get for ideas for building projects to be used in contests, team work, or just plain individual fun.  Problems like: “design and construct a device that will shoot projectiles of newspaper into a bushel basket.  This device will hurl, toss, or otherwise propel a projectile from behind a boundary line toward the target.”  The problems are similar to those used for Odessey of the Mind and are great for scout meetings. Other, shorter problems are listed if you only have an afternoon.  Have fun with this one!
Imagination Celebration Creativity Exercises by Judy Leimback and Joan Vydra.  Having trouble getting started teaching creative thinking?  Use this book to get going.  Easy to use reproducible pages with lessons on basic creativity exercises.  Listing things which are soft and white and all the “ships” you can think of (like friendship).  The authors ask questions like “what does gentle look like?” and “what does green sound like?”  Students are asked to rewrite definitions from the dictionary into their own words.  Other specific tasks are set for students which teach four skills: fluency, flexibility, originality, and elaboration.

Comments Off on Inventions, Creative Thinking, and Problem Solving