Thermal Energy.October 2012

Objectives.

• To identify temperature as the amount of kinetic energy of atoms and molecules.

• To identify different temperature scales and convert from one scale to another.

• To describe heat as the transfer of energy between substances at different temperature.

• To identify the three methods of heat transfer. • To apply the principle of energy conservation to calculate changes in

potential, kinetic and internal energy.• To identify latent and specific heat of substances. • To calculate phase changes of different substances. • To describe thermal expansion.

Temperature

In every day life, temperature is the measure of how hot or cold something is.Many properties of matter change with it. For example, most materials expand when heated.

Temperature Scales

To measure temperature quantitatively we use numerical scales. The most common scale today is Celsius scale. In USA the Fahrenheit scale is also common. And the most important scale for scientific work is the absolute, or Kelvin, scale.

The conversion between the two temperature scales Celsius and Fahrenheit can be written as:

Absolute Temperature

Robert Boyle (1627-1691) established a relation known as Boyle’s Law that states that the volume of a gas is inversely proportional to the absolute pressure applied to it when the temperature is kept constant.

Temperature also affects the volume of a gas. Jacques Charles (1746-1823) found that when the pressure is kept not too high and constant, the volume of a gas increases with temperature at a nearly constant rate.

The graph of volume vs. temperature is a straight line that if projected to low temperatures it crosses the axis at about -2732C. Such a graph can be drawn for any gas, and the straight line always projects back to -2732C at zero volume. At lower temperatures the gas would have a negative volume, which makes no sense. It could be argued that -2732C is the lowest temperature possible. This temperature is called the ABSOLUTE ZERO of temperature and is the basis of the Kelvin scale.

T( 2 K) = T( 2 C) + 273.15

Practice

Among the highest and lowest temperatures recorded are 1362F in the Libyan desert and -1292F in Antarctica. What are these temperatures on the Celsius scale?

152 below zero on Celsius scale is what Fahrenheit temperature?

152 below zero on Fahrenheit scale is what Celsius temperature?

Absolute zero is what temperature on the Fahrenheit scale?

Typical temperatures in the interior of the Earth and the Sun are about 40002C and 15x2C respectively. What are this temperatures in kelvins?

Thermal Equilibrium

If two objects at different temperatures are placed in thermal contact (meaning thermal energy can transfer from one to the other) the two objects will eventually reach the same temperature. They are then said to be in thermal equilibrium.

Kinetic Theory

Amedeo Avogadro (1776-1856) stated that equal volumes of a gas at the same pressure and temperature contain equal numbers of molecules. The number of molecules in one mole of any pure substance is known as Avogadro’s number .

Using the Ideal Gas Law and the number of molecules N related to Avogadro’s number we can get the following relation:

PV=NkT

where (P) Pressure, (V) Volume, (N) Number of molecules, (T) Temperature and (k) is called Boltzmann’s constant.

The analysis of matter in terms of atoms in continuous random motion is called the Kinetic Theory.

Comparing the equations for the average kinetic energy of the molecules in the gas with the Ideal Gas Law we see the two agree if:

This equation tells us that the average translational kinetic energy of the molecules in random motion in an ideal gas is directly proportional to the absolute temperature of the gas.

Heat

Heat is defined as the transferred energy from one object to another because of a difference in temperature.

The common unit for heat is the calorie (cal) and is defined as the amount of heat needed to raise the temperature of one gram of water by 1 Celsius degree.

More often used than the calorie is the kilocalorie (kcal) equivalent to 1000 calories. It is also called a Calorie (With a capital C), and it is by this unit that the energy value of food is specified.

In the British system of units the Btu (British Thermal Unit) is used and corresponds to 0.252 kcal = 1055J.

James Prescott Joule (1818-1889) and others performed a number of experiments that were crucial for establishing the view that heat, like work, represents a transfer of energy.Joule determined that a given amount of work done was always equivalent to a particular amount of heat input. Quantitatively 4.186 joules of work was found to be the equivalent to 1 calorie of heat. This is known as the mechanical equivalent of heat.

Working off the extra Calories

Suppose you throw your caution to the wind and eat too much ice cream and cake on the order of 500 Calories. To compensate, you want to do an equivalent amount of work climbing stairs or a mountain. How much total height must you climb?

Remember W = ΔPE = mgh

NOTE: The human body does not transform energy with 100% efficiency it is more like 20% efficient. So you will actually have to climb 20% of the way (Which is still a lot)

Temperature, Heat and Internal Energy

Using the kinetic theory, we can make a clear distinction between temperature, heat and internal energy (sometimes referred as thermal energy).

Temperature (in kelvins) is a measure of the average kinetic energy of individual molecules.

Internal Energy refers to the total energy of all the molecules in the object.

Heat refers to a transfer of energy from one object to another because of a difference in temperature.

Experiment

Material Needed:

Two identical glasses.Hot Water.Cold Water.Liquid Food Coloring.

Fill your glasses. One should have hot water in it, the other cold water. Pick a color of food coloring.

Put three drops of food coloring in each glass.

Share your observations

Specific Heat

If heat flows into an object, the object temperature rises (assuming no phase change). But how much does the temperature rise? It depends. The amount of heat Q required to change the temperature of a given material is proportional to the mass and the change in temperature.

Q = mcΔT

Where c is a quantity characteristic of the material called its specific heat.

Example

How much heat input is needed to raise the temperature of an empty 20 kg vat made of iron from 102C to 902C? What if the vat is filled with 20 kg of water?

Calorimetry

When different parts of an isolated system are at different temperatures, heat will flow from the part at higher temperature to the part at lower temperature, that is within the system. If the system is isolated no energy is transferred into or out of it.

So the conservation of energy again plays an important role. The heat lost by one part of the system is equal to the heat gained by the other part.

Heat lost = Heat gained

Energy out of one part = energy into another part.

Example

If 0.20kg of tea at 952C is poured into a 150g glass cup initially at 252C what will be the common final temperature T of the tea and cup when equilibrium is reached, assuming no heat flows to the surroundings.

Solution: 862C

Practice

* An automobile cooling system holds 16kg of water. How much heat does it absorb if its temperature rises from 202C to 902C?

Solution: J

* A 35g glass thermometer reads 21.62C before it is placed in 135g of water. When the water and the thermometer come to equilibrium, the thermometer reads 39.22C. What was the original temperature of the water?

Solution: 40.12C

Collaborative Work : HEAT TRANSFER

• The students are assigned in groups of three persons. The sorting method will be by student ID number as per the assistance list.

• Each team will assign one member to be the captain of the team.

• A second member will be the spoke person and will present the results.

• The third member will be the closer and responsible for presenting the group conclusions on the activity.

• The teams will have 25 minutes to complete the research.

• Then in 10 minutes the teams will present the work to the evaluators.

• And after that 5 minutes to present your conclusions.

Heat Transfer Types

The Students must construct a collage of images containing the three (3) types of Heat Transfer

1. Conduction2. Convection3. Radiation

Clearly define in three sections of the collage these different types.

Evaluation

CATEGORY Distinguished (4) Proficient (3) Apprentice (2) Novice (1)

Physic Concepts 30%

Show complete understanding of the physics concepts used. Clearly demonstrates deep understanding of the lesson overall.

Show substantial understanding of the physics concepts used. Demonstrates substantial understanding of the overall lesson.

Show partial understanding of the physics concepts used. Demonstrates partial understanding of the overall lesson.

Show complete lack or very limited understanding of the underlying concepts needed OR are not provided. Demonstrates complete lack of understanding of the overall lesson.

Real World Models 50%

Real world models indicate strong evidence of creativity and imagination.

Real world models shows substantial evidence of creativity and imagination.

Real world models show partial evidence of creativity and imagination.

Models are messy, difficult to understand, OR missing. Real world models lack creativity OR are not provided.

Evaluation Continued

CATEGORY Distinguished (4) Proficient (3) Apprentice (2) Novice (1)

Verbal and non-verbal communication 20%

Accomplishes all of the following: Good tone and voice volume, fluid speaking, adequate body stance, good use of space and resources.

Accomplishes most of the following: Good tone and voice volume, fluid speaking, body stance, good use of space and resources..

Accomplishes just three or two of the following: Good tone and voice volume, fluid speaking, body stance, good use of space and resources.

Accomplishes none or just one of the following: Good tone and voice volume, fluid speaking, body stance, good use of space and resources.

Latent Heat

When a material changes phase from solid to liquid, or from liquid to gas, a certain amount of energy is involved in this change of phase.

The heat required to change 1kg of a substance from solid to liquid state is called HEAT OF FUSION; it is noted with .

The heat required to change from liquid to gas phase is called the HEAT OF VAPORIZATION; it is noted with .

This are generally called LATENT HEATS and is defined as Q = mL. Where m is the mass.

Example: Making Ice

How much energy does a freezer have to remove from 1.5kg of water at 20 2 C to make ice at -12 2 C.

Approach: We need to calculate the energy to reduce the water from 20 to 0 degrees, then to change it to ice, and then to reduce the ice from 0 to -12 degrees.

Solution: 660kJ.

Practice

How much heat is needed to melt 16.50kg of silver that is initially at 20 2 C?

Solution: 5.0 x J

What mass of steam at 100 2 C must be added to 1 kg of ice at 0 2 C to yield liquid water at 20 2 C?

Solution: 1.61 x

EvaporationThe latent heat to change a liquid to a gas is needed not only at the boiling point. Water can change from liquid to gas even at room temperature. This process is called evaporation. The value of the heat of vaporization increases slightly with a decrease in temperature. At 20 2 C for example it is 2450kJ/kg compared to 2260kJ/kg at 100 2 C.

When water evaporates, the remaining liquid cools because the energy required to evaporate comes from the water itself, (Internal Energy) and therefore the temperature must drop.

Evaporation of water from the skin is one of the most important methods the body uses to control temperature.

Heat Transfer: Conduction

When a silver spoon is placed in a hot bowl of soup, the end that you hold becomes hot as well, even though it is not directly in contact with the source of heat. We say the heat has been conducted from the hot end to the cold end.

Heat conduction is carried via molecular collisions.

Some materials are good heat conductors, while others are bad conductors and therefore are good insulators.

Heat Transfer: Convection

Although liquids and gases are not generally not very good conductors of heat, they can transfer heat quite rapidly by convection.

Convection is the process whereby heat flows by the mass movement of molecules from one place to another.

A forced air furnace, in which air is heated and then blown by a fan into a room is an example of forced convection. Natural convection occurs as well, one familiar example is hot air rises.

Heat Transfer: Radiation

Convection and Conduction require the presence of matter as a medium to carry heat. Radiation occurs without any medium at all.

Radiation consists essentially of electromagnetic waves.

The heat received from the sun is the most common example of radiation.

The warmth we receive from fire is mainly radiant energy. Most of the air heated by a fire in a fireplace rises by convection up the chimney and does not reach us.

Collaborative Activity.

Using the world wide web, research how a thermos bottles work.Specify how each type of heat transfer is prevented to keep temperature.

In groups of two, write a small report with your findings

Video: Cooling a Six Pack

Watch the video and then answer the questions that follow.http://www.youtube.com/watch?v=N354fChhjV0

Questions:

1. What is the theory behind the myth of burying a six pack in the sand, pouring gasoline over and set it on fire is supposed to cool the six pack ?

2. Why does Adam proposes checking various traditional cooling methods?

3. How is that the fire extinguisher cools the six pack?

4. Why do you think both Adam and Jamie devices use spiral forms?

5. In the end which way do you think is the most time-cost efficient method to cool a six pack?

Thermal Expansion

Most substances expand when heated and contract when cooled. However the amount of expansion or contraction varies, depending on the material.

Linear Expansion

Experiments indicate that the change in length of almost all solids is approximately directly proportional to the change in temperature.

Where α is a proportionality constant called the coefficient of linear expansion for the particular material.

Volume Expansion

The change in volume of a material which undergoes a temperature change is given by a relation similar to linear expansion.

Where β is the coefficient of volume expansion.

Thermal Pollution and Global Warming

Much of the energy we use in every day life makes use of a heat engine. Over 90% of the electric energy produced in the U.S. is generated at fossil-fuel plants, where oil, coal or gas is burned to move a steam engine.

Thermal Pollution

Thermal Pollution is the heat produced by every heat engine and is absorbed by the environment such as rivers or lakes, or by the air using large cooling towers.

In the case of cooling towers, the output heat raises the temperature of the atmosphere, which affects weather.

Air Pollution

Chemicals released in the burning of fossil fuels gives rise to smog and other problems.

One big problem is the buildup of Carbon Dioxide in Earth’s atmosphere. Carbon Dioxide absorbs infrared radiation that the Earth naturally emits, causing Global Warming, a serious problem that can be addressed by limiting the burning of fossil fuels.

Thermal pollution however is unavoidable. Engineers can try to design and build more efficient engines. But nature imposes a limit to efficiency defined in the second law of thermodynamics that says 100% efficiency is not possible to achieve.

What we can do is use less energy and conserve our fuel resources.

References

• Giancoli , Douglas C. Physics Sixth Edition. USA Pearson 2005

• Serway, Raymond A. Essentials of College Physics. USA Thomson 2007