How Cool is Newton


Author:

Moussa Ndiaye

Unit Title:

How Cool is Newton

Grade:

10

Subject:

Calculus

Estimated Duration:

8 – 53 minutes class Periods

Unit Activities:

Activity 1: Insulation Investigation 

Activity 2: Data Tables and newton’s Law of cooling and heating

Activity 3: Building an Insulated Water Bottle

Activity 4: Data Tables and newton’s Law of cooling and heating

Activity 5: Presentation

Background Knowledge: 

Students should have a practical knowledge of temperature and the flow of heat from areas of high temperature to areas of low temperature. Students should be familiar with plotting points on the Cartesian plane, as well as the significance of independent and dependent axes.

Date:

July 2014

The Big Idea (including global relevance)

Newton’s law of heating and cooling affect every aspect in our lives, whatever it to retain heat or retain cold we need insulation to maintain a comfortable living environment. Insulators have helped humans stay warm or cool for thousands of years. They have also been used to keep food warm and cool. Think of the mitten, people wear mittens when they want to slow down the transfer of body heat to the surrounding cooler environment. People use mittens as a kind of barrier between warm and cold air. Yet some mittens seem to be more effective than others at doing so. Why? Is it the thickness of the mittens, the material the mittens are made of or, could it be a combination of both? Perhaps the size of the mitten plays a part. Larger mittens enable the use of air space trapping molecules, whereas tighter fitting mittens do not. Which works better? Think about the old advice of wearing layers to keep warm. Layered clothing traps air between each layer thus cumulatively adding in the fabric’s insulation effects and reducing the loss of body heat. As the mitten demonstrates, insulation is used to provide a barrier that minimizes the transfer of heat. Insulators can be used to keep items cold or hot. They do so by minimizing conduction, convection, and/or radiation.

The Essential Question

What properties make “good insulators”?

Justification for Selection of Content

In calculus, we learned about Newton's Law of Cooling- that is, the rate at which liquids cool depends on the difference between their temperature and the temperature of the surroundings, or ambient temperature. This is the first year AP Calculus is being taught at 10 grade level. There are no Data available. For Future we will use AP Calculus result to improve this unit.

The Challenge

Using their knowledge of heat transfers, students design an insulated water bottle

The Hook

Student will use a simulator to test Newton’s law of heating and cooling for different material and answer the questions listed in (3.1.01): http://amrita.vlab.co.in/?sub=1&brch=194&sim=354&cnt=4

This video shows how a family use everyday material to insulate their house

http://www.youtube.com/watch?v=Y1XxixvcKh0

Teacher's Guiding Questions
  • How long does it takes for a hot object to cool down?
  • How long does it takes for a cool object to heat up?
  • Can you predict the temperature of a hot object by a certain amount of time?
  • Do you think different materials insulate differently?
  • What devices have you used to decrease or increase the rate of heat transfers?
  •  How thick should the insulation of the bottle be?
  • Does the bottle primarily hold hot or cold liquids?
  • What is the estimated time frame for which the insulation should maintain liquid temperature?

ACS (Real world applications; career connections; societal impact)

Heat transfer is a broad topic used in many branches of engineering. For example, mechanical engineers who design engines from steam locomotives to modern internal combustion engines rely on a detailed understanding of how heat moves through all types of matter. Industrial engineers use heat transfer concepts to design climate control systems for manufacturing facilities, such as foundries or refrigerated food production facilities, which integrate temperature-sensitive human workers with extreme temperature processes. In crime scenes the cooling law can indicate the time of death given the probable body temperature at time of death and the current body temperature, as well as known cooling rate constant and ambient temperature.

Engineering Design Process (EDP)

Student will investigate which variable insulate the bottle the most and decide what combination of variables would give them a better insulation. They will analyze, discuss data, brainstorm at least three type of insulated bottles, build an insulated bottle, revise and refine if necessary to get more efficient insulated bottle.

Unit Academic Standard

The College Board state that:

  • Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation, and should be able to use derivatives to solve a variety of problems.
  • Students should be able to communicate mathematics and explain solutions to problems both verbally and in written sentences.
  • Students should be able to model a written description of a physical situation with a function, a differential equation, or an integral.
  • Students should be able to use technology to help solve problems, experiment, interpret results, and support conclusions.
  • Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
Unit Activities

Lesson 1: Not Hot Enough

  • Activity 1: Insulation Investigation
  • Activity 2: Data Tables and newton’s Law of cooling and heating

Lesson 2: Keeping It Cool

  • Activity 3: Building an Insulated Water Bottle
  • Activity 4: Data Tables and newton’s Law of cooling and heating
  • Activity 5: Presentation
Where the CBL and EDP appear in the Unit

Lesson 1: Not Hot Enough

  • Activity 1: Insulation Investigation (EDP)
  • Activity 2: Data Tables and newton’s Law of cooling and heating (EDP)

Lesson 2: Keeping It Cool

  • Activity 3: Building an Insulated Water Bottle (EDP, CBL)
  • Activity 4: Data Tables and newton’s Law of cooling and heating (EDP, CBL)
Misconceptions

An exponential decay is a solution of differential equation dy/dx= kx

Additional Resources

This is a hands-on-activity on Newton's Law of cooling developed by, Polytechnic Institute of New York University

http://www.teachengineering.org/view_activity.php?url=collection/nyu_/activities/nyu_cooling/nyu_cooling_activity1.xml

This is a seven grade science PBL in State of Main

http://www.powersleuth.org/docs/EHM%20Lesson%207FT.pdf

Pre-Unit Assessment Instrument
Post-Unit Assessment Instrument
How to Make This a Hierarchical Unit

This is a modified unit from 7th grade science PBL http://www.powersleuth.org/docs/EHM%20Lesson%207FT.pdf