Content Benchmark P.12.C.5
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Students know the relationship between heat and temperature. I/S

Students often view heat and temperature to be synonymous; they are not. This is a major misconception that will prevent students from fully understanding energy transfer. In basic terms heat is a transfer of energy from hot to cold objects. On the other hand, temperature is a quantity that tells how hot or cold something is compared to a standard.

Heat may be defined as energy in transit from a high temperature object to a lower temperature object. An object does not possess "heat"; the appropriate term for the microscopic energy in an object is internal energy. The internal energy of an object may be increased by transferring energy from a higher temperature (hotter) object, this is commonly called heating. However, the object can absorb heat and undergo no change in temperature. A change in temperature is designated by the type of energy storage (i.e., potential or kinetic). See the concept map below for examples of heat transfer.

Figure 1. Concept map 1 shows examples of heat transfer. (from http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatranex.html#c1)

In an ideal gas, temperature is a measure of the average translational (picture “sliding” molecules) kinetic energy associated with the disordered microscopic motion of atoms and molecules. In solids and liquids, molecules are more constrained, and in addition to their kinetic energy, they have a significant component of potential energy. Therefore, the calculation of temperature is more complex. In general terms, temperature measures how “hot” or how “cold” something is compared to a standard. Nearly all matter expands when its temperature increases and contracts when its temperature decreases, as the matter approaches thermal equilibrium.

The common thermometer works according to thermal equilibrium. The thermometer measures temperature by showing the expansion and contraction of a liquid, most often mercury or alcohol, in a glass tube with gradations. The faster the molecules within the material are moving, the more they “bump” into the liquid in the thermometer. This is a transfer of kinetic energy from the material to the liquid within the thermometer. The liquid in the thermometer continues to expand or contract until it reaches thermal equilibrium with the material in which it is measuring. Thermometers can not measurement the total amount of internal energy in an object, only the average translational kinetic energy.

To learn more about thermal equilibrium go to
http://www.grc.nasa.gov/WWW/K-12/airplane/thermo0.html

The Celsius scale is the most commonly used temperature scale. The Celsius scale is based on water at standard atmospheric pressure assigning a value of 0° for freezing water and 100° for boiling water. The gradations between freezing and boiling water is divided into 100 equal parts. Gradations on the Celsius scale and the Kelvin (absolute temperature) scale are equivalent. On the Kelvin scale the number 0 is assigned to the lowest possible temperature, absolute zero. At absolute zero a substance has no kinetic energy to give up.

To learn more about temperature and scales go to
http://www.eo.ucar.edu/skymath/tmp2.html#Dev.

Figure 2. A Florentine thermoscope, one of the first thermometers. (from http://www.eo.ucar.edu/skymath/tmp2.html#Dev)

Heat and temperature are related in terms of internal energy. The internal energy of a substance is a measure of the amount of kinetic and potential energy. Their relationship is governed by the laws of thermodynamics.

The First Law of Thermodynamics is explained through energy transfer (both heat and mechanical energy as work). The law states that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system. This is written as:

Figure 3. The equation for the First Law of Thermodynamics. (from http://hyperphysics.phy-astr.gsu.edu/hbase /thermo/firlaw.html#c1)

The change in the internal energy (ΔU) of a system is a change in the potential and kinetic energy of the system. The relationship between heat (energy transfer) and temperature is found in the type of energy storage, either potential (no gain in temperature) or kinetic (gain in temperature).

To learn more about internal energy go to
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/inteng.html#c2.

The Second Law of Thermodynamics designates that, in the absence of an external effort, heat flows only from higher to lower temperature, and that some energy is lost to the environment. The amount of heat that is lost to the environment depends greatly upon the efficiency of the system. This heat loss adds to the disorder of a system, this disorder is called entropy.

To learn more about the Second Law of Thermodynamics go to
http://www.grc.nasa.gov/WWW/K-12/airplane/thermo1.html

The SI unit for heat is the joule (J). The most common form of quantifying heat is with the measurement of a calorie. The calorie is the amount of heat needed to raise 1g of water by 1°C. Food Calories, 1000 calories, are also a common quantifier of energy. The relationship between calories and joules is that 1 calorie is equal to 4.187 J. The energy value in food is determined by burning the food and measuring the quantity of internal energy that is released as heat.

Heat can be measured as sensible heat and latent heat. Sensible heat can be calculated through the equation Q = mcΔT, where the mass (kg) of the material multiplied by the specific heat of the material multiplied by the change in temperature of the material. Specific heat is the measure of the amount of energy required to raise the temperature of a unit of mass of a substance by one degree. This is a direct relationship between temperature change and heat.

To learn more about specific heat go to
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html#c1

Latent heat refers to the amount of energy that must be absorbed or emitted in order for a material to complete a phase change. The equation for latent heat is Q_f = mH_f and Q_v = mH_v, where the mass (kg) of the material multiplied by the latent heat of fusion (J/kg) [or vaporization (J/kg)] is equal to the amount of energy required for the phase change. The temperature of a material does not change during a phase change even though the material is being heated. If energy is added then the internal energy of the system is increasing as heating occurs, but the energy is stored as potential energy. This is why it is undetectable with a thermometer.

To learn more about latent heat and phase change go to
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html#c1.

Heat transfer occurs because there is a temperature difference between two objects and there are three basic mechanisms in which heat is transferred between objects of different temperature: (1) conduction, (2) convection, and (3) radiation.

• Conduction occurs within materials and between materials that are in direct contact. Materials that conduct heat well are known as conductors. Materials that are poor conductors are referred to as insulators.

To learn more about conduction go to
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.html#c2.

• Convection occurs by currents through a fluid. Fluids may be defined as a liquid or gas. Convection cells are caused by heating and changes in density. As a heated medium expands it becomes less dense than the surrounding material, this is what causes it to rise.

To learn more about convection go to
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.html#c3.

• Radiation is the transfer of energy (including heat) through electromagnetic waves. This form of heat does not require a medium in which to travel. Energy is carried away from the emitting object.

To learn more about radiation go to
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html#c2.

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Content Benchmark P.12.C.5

Students know the relationship between heat and temperature. I/S

Common misconceptions associated with this benchmark:

1. Students incorrectly believe that “heat is an object or something other than energy.”

Students often want to view heat as a property of a material. This is not a new misconception as the word calorie stems from caloric, which was once thought to be an invisible heat fluid. Today we know that heat is one of three ways in which energy is transferred.

To learn more about heat as a form of energy transfer go to
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heat.html#c1.

2. Students incorrectly think that when objects are heated the particles expand and when objects are cooled the particles contract.

Students need to realize that thermal expansion and contraction doesn’t occur within the molecule. The atoms do not expand and contract. Expansion is due to the increase in vibrational, rotational, and translational kinetic energy gain. If you were to drop a box of golf balls off the roof of a second story building the balls, upon hitting the ground, would bounce and scatter. This is similar to thermal expansion in that the golf balls, like the material undergoing thermal expansion, do not grow in size as they increase the amount of space between other balls.

To learn more about thermal expansion go to
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp.html#c1
To learn how to use thermal expansion too your advantage, go to
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/jarlid.html#c1.

3. Students may incorrectly think that temperature depends on the material
(i.e., metal is colder than fabric or that blankets and coats are warm objects because clothes keep you warm.

The above misconception stems from the thought that energy is a property of an object and the lack of understanding about how energy is transferred. A tile floor will “feel” colder. This is true, but not because tile is an inherently “cold” material. This is true because tile is a good conductor of heat compared to carpet. While students walk on a tile floor energy transfers, according to the Second Law of Thermodynamics, from their feet to the floor. This also occurs with a carpeted floor just not as quickly because carpet has trapped air which is an insulator.

To learn more about thermal conductors and insulators go to
http://hypertextbook.com/physics/thermal/conduction/.

4. Students incorrectly believe that temperatures are additive.

“If you mix 40 degree water with 40 degree water you get 80° water, or more than 40° water.” This is a common misconception that occurs because students lack a complete understanding of the concept of internal energy and work. If you were to mixing two sources of water at the same temperature then the resulting temperature will be the same. This is an offshoot of the Zeroth Law of Thermodynamics, which concerns thermal equilibrium. Also, if the amounts of water are different then their resulting temperature will be a function of their masses and original temperatures.

To learn more about the Zeroth Law of Thermodynamics, go to
http://www.grc.nasa.gov/ WWW/K-12/airplane/thermo0.html

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Content Benchmark P.12.C.5

Students know the relationship between heat and temperature. I/S

Sample Test Questions

1^st Item Specification: Describe heat and temperature using kinetic energy of particles.

Depth of Knowledge Level 1

1. The sum of the kinetic and potential energies of an object’s molecules is referred to as the object’s
1. temperature.
2. heat of fusion.
3. specific heat.
4. thermal (internal) energy

2. A thermometer is a device that measures
1. average heat transferred.
2. average internal energy.
3. average kinetic motion.
4. average molecular volume.

3. Of the following, which state of matter refers to a material with the lowest amount of average translational kinetic energy of its molecules?
1. Solid
2. Liquid
3. Gas
4. Plasma

4. Two blocks of metal are placed into an insulated container and there is a net transfer of heat between the blocks. Which of the following statements is true?
1. The blocks started with the same temperature.
2. The blocks have a different specific heat.
3. The blocks started with different temperatures.
4. The blocks have the same melting point.

5. If material X has a higher temperature than material Y, then the molecules in material X are moving at
1. an average slower speed then those of material Y.
2. the same speed of material Y.
3. an average greater speed then those of material Y.
4. average speeds that are not comparable to material Y.

Depth of Knowledge Level 2

6. The graph below represents the temperature of 6.0 kg of water as a function of energy added to the substance. Use the graph to answer the following question.

(From http://itl.chem.ufl.edu/2045_s00/lectures/lec_f.html )

During which intervals, shown on the graph, is the average potential energy of the molecules of the material increasing?

1. AB and CD
2. BC and DE
3. CD and DE
4. AB and EF

7. The graph below represents the temperature of 6.0 kg of water as a function of energy added to the substance. Use the graph to answer the following question.

(From http://itl.chem.ufl.edu/2045_s00/lectures/lec_f.html )

During which intervals, shown on the graph, is the average translational kinetic energy of the molecules of the material increasing?

1. AB and CD
2. CD and DE
3. BC and CD
4. AB and DE

8. If you mix 50 g of water at 100°C with 50 g of water at 0°CC what estimate will MOST likely be the resulting temperature of the 100 g of water?
1. 100°C
2. 75°C
3. 50°C
4. 25°C

9. Why does a ceramic tile floor feel colder than a carpeted floor when they are in the same room?
1. A ceramic tile floor has less heat than a carpeted floor.
2. A carpeted floor feels warmer because it has a higher temperature.
3. A ceramic tile floor is a better thermal conductor than a carpeted floor.
4. A carpeted floor transfers energy faster than a ceramic tile floor.

10. Water is spilled on a table on a hot summer day. Which statement best describes what is occurring as water evaporates off of the surface?
1. As water evaporates it requires energy causing the temperature of the
   surface to increase.
2. Water evaporating will transfer energy causing the surface to change into
   a different state of matter.
3. The water that evaporates will immediately condense back onto the surface.
4. As water evaporates it draws energy away from the surface causing a
   decrease in surface temperature.

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Content Benchmark P.12.C.5

Students know the relationship between heat and temperature. I/S

Answers to Sample Test Questions

1. D, DOK Level 1
2. C, DOK Level 1
3. A, DOK Level 1
4. C, DOK Level 1
5. C, DOK Level 1
6. B, DOK Level 2
7. A, DOK Level 2
8. C, DOK Level 2
9. C, DOK Level 2
10. D, DOK Level 2

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Content Benchmark P.12.C.5

Students know the relationship between heat and temperature. I/S

Intervention Strategies and Resources

The following is a list of intervention strategies and resources that will facilitate student understanding of this benchmark.

1. ThePhysicsFront.org Lessons, Activities, and Resources
The National Science Foundation, American Association of Physics Teachers, and National Science Digital Library has created ThePhysicsFront.org , a Web site for Physics Educators that has a collection of high-quality, ready to use lesson plans. The lesson plans are complete with labs, activities and further resources.

Lesson plans and activities for heat and temperature can be found at
http://www.thephysicsfront.org/search/search.cfm

2. HyperPhysics Web Site
Georgia State University’s Hyperphysics (http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html) Web site is one of the most complete physics content resources available. The site is a lattice of concept maps with hyperlinks to each topic. Most topics have an outline of content with links to further content, applets for practice problems, and further resources. Students can click on concepts within the concept maps to view more information, and see the interconnections throughout basic physics concepts

The section that deals with heat and temperature is
http://hyperphysics.phy-astr.gsu.edu/hbase/heacon.html#heacon

3. Hands-On-Physics Problem Solving Unit
The Concord Consortium’s Hands-On-Physics Web site offers a unit on heat and temperature. The unit presents several projects which will help your students understand heat. Students start by learning how to measure temperature. As the unit unfolds, students are introduced to the major concepts of heat and temperature through a series of interesting projects.

For information about Hands-On-Physics go to http://hop.concord.org/h1/info/h1i.html

4. Interactive Heat Experiment
Davidson University offers an exercise that explores the changes that occur to a substance during heating. The site is linked to an applet that allows students to manipulate variables within a phase change experiment. At the outset of the experiment, a cylinder is equipped with a movable barrier and contains 0.200 mole of a pure solid. The barrier is exposed to the atmosphere and thus the material in the cylinder experiences a constant pressure at all times during the experiment. During the experiment students can view temperature time graph that plots a phase change graph. Questions follow the graph to check for understanding.

To learn more go to
http://www.chm.davidson.edu/ChemistryApplets/PhaseChanges/HeatingCurve.html.

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