+

The Strength of Modeling in ScienceFocus: Energy in temperature changes and changes of state

+

The Modeling Approach Applied to Energy…

+Energy is conserved.

We have a very clear understanding of what this statement means, and how it applies to scientific thinking and problem solving.

Students don’t always understand it as clearly.

+The “go to” Lab

Ice is put into a beaker and the beaker is put on a warming plate.

A temperature probe is inserted into the ice in the beaker.

Vernier software LoggerPro begins to record temperature changes over time – students understand that energy is constantly being added to the system from the hot plate.

+Heating Curve

Curve generated from data:

+Observations

Label each plateau:

Solid to liquid Liquid to vapor

(gas)

Liquid only

+Pose the obvious question:

Where did all of that energy go?

It increased the temperature.

It “melted it”.

Energy wasn’t really being added yet.

+“Aha” Moment

It all becomes clear when you get responses like these that there are misconceptions about energy transfer and its role at the particle level.

What to do next?

+Energy “modeling” style

Compare energy to money – you cannot have money in your savings account and your checking account at the same time.

Energy cannot be causing two different changes at once… it either causes a phase change or a temperature change.

+Your turn!

On your group’s white board, Draw particle representations for each portion of your graph.

+Remember the plateaus?

Solid to liquid

Liquid to vapor (gas)

+Phase Energy

When the temperature doesn’t change, but you understand energy has been added to the system, maybe it caused a change of phase.

We know it didn’t cause a change in temperature because we can read it from the graph.

There are two places on the graph that show change of phase because there are two temperature plateaus.

+Temperature Changes

Temperature change

+What happens in a temperature change?

As energy is added, the temperature increases.

This means that, on average, the particles are moving faster and faster.

The energy that is coming into the system is going into the “thermal” account and speeding up the motion of the particles, but they stay in the same state of matter.

+Where do we go from here?

The heating curve for water is used to show change in every chemistry text book, and it is a great graphical representation of the energy changes.

The modeling program has a second approach to graphically showing changes in energy –” Energy Bar Charts”.

+Constructing an Energy Bar

ChartA cup of hot coffee cools as it sits on the table.

1. Determine what is in the system

Everything else makes up the surroundings

cup coffee

+Decide whether Ech is involved

In this case, you start with coffee and end with coffee; particles are not rearranged to form new substances

So, ignore Ech for now.

+Assign values to Eph

Due to interactions between particles, the energy stored due to the arrangement of particles is ranked:solids < liquids < gases

We choose to represent these phases by using: Solids = 1 bar Liquids = 2 bars Gases = 4 bars

+Assign values to Eph

Use two Eph bars before and after

cup coffee

+Choose bars for Eth depending on temperature Use 4 bars for hot coffee and 2 bars for room temp

coffee

Other values might also work; try to be consistent in your representations

cup coffee

+Now show energy transfer

Final situation has 2 less bars of E than initial; 2 bars had to leave the system

+Now, consider phase change

A tray of ice cubes (-8 ˚C) is placed on the counter and becomes water at room temperature

What do we know about the situation? The system is the tray of ice cubes. The solid water turns to liquid water - no change

in Ech

The Eph increases (solidliquid)

The Eth increases (temp rises)

Now represent these changes in bar graph.

+Initial & Final States Choice of bars for Eth arbitrary, but consistent.

We used 2 bars for room temp and 1 bar for cold soda before.

Temp < 0˚C should be < 1 bar.

+Account for Energy

Energy must flow into system via heating

+Breaking It Down

In the beginning if students struggle with the energy bar diagrams. I break them apart into separate ones that are part of a sequence.

After they have the sequence, we summarize by going from the first picture directly to the last and showing the overall change.

+Adding the quantitative portion…

DH = mCDTUse the equation with

temperature change b/c temperature is changing

= DH mHf

= DHmHfv

+Tying it all together.

When students are asked to solve thermal energy problems, they are required to show a heating curve and an energy bar diagram.

Let’s look at the white boards…

+In Conclusion - What is Modeling?

Modeling is not a set curriculum

Follows the Modeling Cycle

Model Development Stage occurring in this lab Students see a phenomenon Students plan experiment Students analyze data Students present results to class Results are generalized

Uses multiple representations of content to develop a conceptual model

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Symbolic Representations

Physical System

Mental Model

Verbal

Algebraic

Diagrammatic

Graphical

+Modeling Success in Literature

Figure 1 shows that traditional high school instruction (lecture, demonstration, and standard laboratory activities) has little impact on student beliefs, with an average FCI posttest score of about 42%, still much below the Newtonian threshold[1] [2]. This failure of traditional instruction is largely independent of the instructor’s knowledge, experience and teaching style.

FCI %

Modeler Modeler

+For more information about Modeling…

http://modeling.asu.edu/

http://modelinginstruction.org/