**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 7^{th} grade science PBL http://www.powersleuth.org/docs/EHM%20Lesson%207FT.pdf