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Monday, August 26, 2013

Proving Trigonometric Identities

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Graphs of the Sine and Cosine Function

Lesson Objectives

  • Quick Review of Trigonometric Identities
  • Some Steps in Proving/Verifying Identities
  • Some hints and suggestions for better proving
  • Some problems and exercises involving proving identities
  • How to get proficient at verifying identities
  • Never give up, every identity is different. You will soon succeed.

Proving Trigonometric Identities Lecture PDF

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Trigonometric Identities

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Graphs of the Sine and Cosine Function

Lesson Objectives

  • Definition of Identity
  • Enumerate Reciprocal Identities
  • Enumerate Quotient Identities
  • Enumerate Pythagorean Identities
  • Enumerate Even-Odd Identities
  • Could successfully analyze, verify and prove Identities

Trigonometric Identities Lecture PDF

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Thursday, August 22, 2013

Graphs of Other Trigonometric Functions

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Graphs of the Sine and Cosine Function

Lesson Objectives

  • Able to plot the different Trigonometric Graphs
  • Graph of Tangent Function (y = f(x) = tanx)
  • Graph of Cotangent Function (y = f(x) = cotx)
  • Graph of Secant Function (y = f(x) = secx)
  • Graph of Cosecant Function (y = f(x) = cscx)
  • Define the Maximum and Minimum value in a graph
  • Generalized Trigonometric Functions
  • Graphs of y = sinbx
  • Graphs of y = sin(bx + c)
  • Could find the Period of Trigonometric Functions
  • Could find the Amplitude of Trigonometric Functions
  • Variations in the Trigonometric Functions

Graphs of Other Trigonometric Functions Lecture PDF

Graphs of Other Trigonometric Functions Lecture PPT

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Graphs of the Sine and Cosine Functions

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Graphs of the Sine and Cosine Function

Lesson Objectives

  • Able to plot the different Trigonometric Graphs
  • Graph of Sine Function (y = f(x) = sinx)
  • Graph of Cosine Function (y = f(x) = cosx)
  • Define the Maximum and Minimum value in a graph
  • Generalized Trigonometric Functions
  • Graphs of y = sinbx
  • Graphs of y = sin(bx + c)
  • Could find the Period of Trigonometric Functions
  • Could find the Amplitude of Trigonometric Functions
  • Variations in the Trigonometric Functions

Graphs of the Sine and Cosine Functions Lecture PDF

Graphs of the Sine and Cosine Functions Lecture PPT

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Wednesday, August 21, 2013

Trigonometric Function of General Angles

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Trigonometric Function of General Angles

Lesson Objectives

  • Trigonometric Functions of Angles
  • Trigonometric Function Values
  • Could find the Six Trigonometric Functions
  • The Signs of Trigonometric Functions
  • Could easily determine the signs of each Trigonometric Functions
  • Trigonometric Functions Quadrantal Angle
  • Solve problems involving Quadrantal Angles
  • Find Coterminal Angles
  • Learn to solve using reference angle
  • Solve problems involving Trigonometric Functions of Common Angles
  • Solve problems involving Trigonometric Functions of Uncommon Angles

LESSON OUTLINE:

  • Finding trigonometric function values of any angle
  • Finding the six trigonometric functions
  • Using the reference angle
  • Using the same triangle idea
  • The Signs of Trigonometric Functions
  • Trigonometric Functions Quadrantal Angle
  • Trigonometric Functions of Real Numbers
  • Trigonometric Functions of Any Angle
  • Evaluating Trigonometric Functions
  • Using Coterminal Angle to Find the Exact Value of a Trigonometric Funcion
  • Trigonometric Functions of Common Angles
  • Trigonometric Functions of “Uncommon” Angles
  • Seatwork
  • Homework

Trigonometric Function of General Angles Lecture

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Trigonometry: Angles and Measurement

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Trigo: Angles and Measurement

Lesson Objectives

  • Learn Definition and History of Trigonometry
  • Know Some Introductory Concepts
  • Define angles and how they are measured
  • Changing Degree Measure to Radian Measure
  • Changing Radian Measure to Degree Measure
  • Solve problems involving the Sector Angle or Arc Length
  • Solve problems involving Area of a Sector of a Cirle
  • Solve problems involving Angular Velocity

LESSON OUTLINE:

  • Definition
  • History of Trigonometry
  • Angles in Standard Position
  • Positive and Negative Angles
  • Measuring Angles
  • Changing from Degree to Radian and vice versa
  • Degree Minute and seconds
  • Measuring Arc Length
  • Finding the sector angle
  • Area of a sector of a circle
  • Angular Velocity
  • Seatwork
  • Homework

Angles and Measurement Lecture

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Tuesday, August 20, 2013

Differential Table - Differentiation Formulas

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Trigonometry Handouts, Cheats and Worksheets
This post is intended for the compilation of complete table of Differential. Let this be your guide for the correct and successful differentiation of every problems in Differential Calculus. I'm sure this will make your homework easy and exciting to solve. Let me know if you want to add differential formulas that I missed.

There is a download button at the end of the post, make sure to have a copy for your reference.

Differentiation Formulas

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©2013 www.FroydWess.com

Sunday, August 18, 2013

Trigonometry Handouts, Cheats and Worksheets

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Trigonometry Handouts, Cheats and Worksheets
Due to time constraint, I failed to add lectures for Trigonometry. I want you to understand that I am adding notes only during my free time. For now, this page will be the temporary location for trigonometry concerns including handouts, cheats, worksheets that you can download for future references.

I am confident that all lectures will be added soon.

Fundamental Trigonometric Table

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Trigonometric Cheat Sheet

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credit: Paul Dawkins©2013 www.FroydWess.com

Saturday, August 17, 2013

Chapter Quiz: Temperature and Kinetic Theory- MCQs

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Chapter Quiz: Temperature and Kinetic Theory- MCQs
Begin and Good luck!

1. Which is the largest unit: one Celsius degree, one Kelvin degree, or one Fahrenheit degree?

  • A) one Celsius degree
  • B) one Kelvin degree
  • C) one Fahrenheit degree
  • D) both one Celsius degree and one Kelvin degree
  • E) both one Fahrenheit degree and one Celsius degree

2. It turns out that – 40°C is the same temperature as – 40°F. Is there a temperature at which the Kelvin and Celsius scales agree?

  • A) yes, at 0 °C
  • B) yes, at -273 °C
  • C) yes, at 0 K
  • D) no

3. You may notice that if a mercury-in-glass thermometer is inserted into a hot liquid, the mercury column first drops, and then later starts to rise (as you expect). How do you explain this drop?

  • A) the mercury contracts before the glass contracts
  • B) the glass contracts before the mercury contracts
  • C) the mercury contracts before the glass expands
  • D) the glass expands before the mercury expands

4. Two drinking glasses are stuck, one inside the other. How would you get them unstuck?

  • A) run hot water over them both
  • B) put hot water in the inner one
  • C) run hot water over the outer one
  • D) run cold water over them both
  • E) break the glasses

5. A steel tape measure is marked such that it gives accurate length measurements at room temperature. If the tape measure is used outside on a very hot day, how will its length measurements be affected?

  • A) measured lengths will be too small
  • B) measured lengths will still be accurate
  • C) measured lengths will be too big

6. Metals such as brass expand when heated. The thin brass plate in the movie has a circular hole in its center. When the plate is heated, what will happen to the hole?

  • A) gets larger
  • B) gets smaller
  • C) stays the same
  • D) vanishes

clip_image002[4]

7. A steel ring stands on edge with a rod of some material inside. As this system is heated, for which of the following rod materials will the rod eventually touch the top of the ring?

  • A) aluminum
  • B) steel
  • C) glass
  • D) aluminum and steel
  • E) all three

clip_image004[4] clip_image006[4]

8. You want to take apart a couple of aluminum parts held together by steel screws, but the screws are stuck. What should you do?

  • A) heat the thing up
  • B) cool the thing down
  • C) blow the thing up

9. A grandfather clock uses a brass pendulum to keep perfect time at room temperature. If the air conditioning breaks down on a very hot summer day, how will the grandfather clock be affected?

  • A) clock will run slower than usual
  • B) clock will still keep perfect time
  • C) clock will run faster than usual

10. Which has more molecules – a mole of nitrogen (N2) gas or a mole of oxygen (O2) gas?

  • A) oxygen
  • B) nitrogen
  • C) both the same

11. Which weighs more – a mole of nitrogen (N2) gas or a mole of oxygen (O2) gas?

  • A) oxygen
  • B) nitrogen
  • C) both the same

12. Two identical cylinders at the same temperature contain the same gas. If A contains three times as much gas as B, which cylinder has the higher pressure?

  • A) cylinder A
  • B) cylinder B
  • C) both the same
  • D) it depends on temp. T

13. Two identical cylinders at the same pressure contain the same gas. If A contains three times as much gas as B, which cylinder has the higher temperature?

  • A) cylinder A
  • B) cylinder B
  • C) both the same
  • D) it depends on temp. T

14. Two identical cylinders at the same temperature contain the same gas. If B has twice the volume and half the number of moles as A, how does the pressure in B compare with the pressure in A?

  • A) PB = 1/2 PA
  • B) PB = 2 PA
  • C) PB = 1/4 PA
  • D) PB = 4 PA
  • E) PB = PA

15. A plastic soda bottle is empty and sits out in the sun, heating the air inside. Now you put the cap on tightly and put the bottle in the fridge. What happens to the bottle as it cools?

  • A) it expands and may burst
  • B) it does not change
  • C) it contracts and the sides collapse inward
  • D) it is too dark in the fridge to tell

16. What happens to the volume of a balloon if you put it in the freezer?

  • A) it increases
  • B) it does not change
  • C) it decreases

credit: Giancoli Physics©2013 www.FroydWess.com

Chapter Quiz: Sound - MCQs

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Chapter Quiz: Sound - MCQs
Begin and Good luck!

1. When a sound wave passes from air into water, what properties of the wave will change?
  • A)      the frequency f                     
  • B)     the wavelength λ
  • C)      the speed of the wave                   
  • D)      both f and λ
  • E)      both vwave and λ
2. We just determined that the wavelength of the sound wave will change when it passes from air into water.   How will the wavelength change?
  • A)      wavelength will increase     
  • B)      wavelength will not change                    
  • C)      wavelength will decrease
3. Do sound waves travel faster in water or in ice?
  • A)      water                                                
  • B)      ice    
  • C)      same speed in both            
  • D)      sound can only travel in a gas
4. Do you expect an echo to return to you more quickly or less quickly on a hot day, as compared to a cold day?
  • A)      more quickly on a hot day   
  • B)      equal times on both days                                 
  • C)      more quickly on a cold day
5. If you fill your lungs with helium and then try talking, you sound like Donald Duck.   What conclusion can you reach about the speed of sound in helium?
  • A)      speed of sound is less in helium
  • B)      speed of sound is the same in helium
  • C)      speed of sound is greater in helium
  • D)      this effect has nothing to do with the  speed in helium
6. You drop a rock into a well, and you hear the splash 1.5 s later.  If the depth of the well were doubled, how long after you drop the rock would you hear the splash in this case?
  • A)      more than 3 s later                        
  • B)      3 s later
  • C)      between 1.5 s and 3 s later 
  • D)      1.5 s later
  • E)      less than 1.5 s later

7. You stand a certain distance away from a speaker and you hear a certain intensity of sound.  If you double your distance from the speaker, what happens to the sound intensity at your new position?
  • A)      drops to 1/2 its original value 
  • B)      drops to 1/4 its original value
  • C)      drops to 1/8 its original value
  • D)      drops to 1/16 its original value               
  • E)      does not change at all
         
8. You hear a fire truck with a certain intensity, and you are about 1 mile away.   Another person hears the same fire truck with an intensity that is about 10 times less.   Roughly how far is the other person from the fire truck?

  • A)      about the same distance               
  • B)      about 3 miles
  • C)      about 10 miles                      
  • D)      about 30 miles
  • E)      about 100 miles

9. When Mary talks, she creates an intensity level of 60 dB at your location.  Alice talks with the same volume, also giving 60 dB at your location.  If both Mary and Alice talk simultaneously from the same spot, what would be the new intensity level that you hear?

  • A)      more than 120 dB                         
  • B)     120 dB
  • C)      between 60 dB and 120 dB
  • D)      60 dB
  • E)      less than 60 dB
10. A quiet radio has an intensity level of about 40 dB.   Busy street traffic has a level of about 70 dB.   How much greater is the intensity of the street traffic compared to the radio?
  • A)      about the same                     
  • B)      about 10 times
  • C)      about 100 times                    
  • D)      about 1000 times
  • E)      about 10,000 times

11. Intensity level is given by β = 10 log(I/I0) with I0 = 10-12 W/m2.  The usual threshold of human hearing is defined as intensity level of β = 0 dB.  What does this actually mean in terms of sound intensity?
  • A)      intensity is undefined at that level
  • B)      intensity is 100 W/m2
  • C)      intensity is 0.0 W/m2
  • D)      intensity is 10-12 W/m2
  • E)      intensity is 1.0 W/m2

12. You have a long pipe and a short pipe.   Which one has the higher frequency?

  • A)      the long pipe                        
  • B)      the short pipe
  • C)      both have the same frequency    
  • D)      depends on the speed of sound in the pipe

13. A wood whistle has a variable length.  You just heard the tone from the whistle at maximum length.  If the air column is made shorter by moving the end stop, what happens to the frequency?

  • A)      frequency will increase        
  • B)      frequency will not change
  • C)      frequency will decrease

14. If you blow across the opening of a partially filled soda bottle, you hear a tone.  If you take a big sip of soda and then blow across the opening again, how will the frequency of the tone change?

  • A)      frequency will increase        
  • B)      frequency will not change
  • C)      frequency will decrease

15. You blow into an open pipe and produce a tone.  What happens to the frequency of the tone if you close the end of the pipe and blow into it again?

  • A)      depends on the speed of sound in the pipe
  • B)      you hear the same frequency
  • C)      you hear a higher frequency
  • D)      you hear a lower frequency

16. When you tune a guitar string, what physical characteristic of the string are you actually changing?

  • A)      the tension in the string
  • B)      the mass per unit length of the string
  • C)      the composition of the string
  • D)      the overall length of the string
  • E)      the inertia of the string

17. Speakers A and B emit sound waves of λ = 1 m, which interfere constructively at a donkey located far away (say, 200 m).   What happens to the sound intensity if speaker A steps back 2.5 m?

  • A)      intensity increases               
  • B)      intensity stays the same
  • C)      intensity goes to zero
  • D)      impossible to tell
18. The traces below show beats that occur when two different pairs of waves interfere.  For which case is the difference in frequency of the original waves greater?
  • A)      pair 1                                               
  • B)      pair 2
  • C)      same for both pairs                       
  • D)      impossible to tell by just looking
image003
 19. Observers A, B, and C listen to a moving source of sound.  The location of the wave fronts of the moving source with respect to the observers is shown below.  Which of the following is true?
  • A)      frequency is highest at A 
  • B)      frequency is highest at B
  • C)      frequency is highest at C
  • D)      frequency is the same at all three points
image004
20. You are heading toward an island in a speedboat and you see your friend standing on the shore, at the base of a cliff.  You sound the boat’s horn to alert your friend of your arrival.  If the horn has a rest frequency of f0, what frequency does your friend hear?
  • A)      lower than f0                                                            
  • B)      equal to f0
  • C)      higher than f0
21. In the previous question, the horn had a rest frequency of f0, and we found that your friend heard a higher frequency f1 due to the Doppler shift.  The sound from the boat hits the cliff behind your friend and returns to you as an echo.  What is the frequency of the echo that you hear?
  • A)      lower than f0                                   
  • B)      equal to f0
  • C)      higher than f0 but lower than f     D)      equal to f1
  • E)      higher than f1

credit: Giancoli Physics©2013 www.FroydWess.com

Monday, August 12, 2013

Applied Physics Lecture: Electric Charge and Electric Field

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Applied Physics Lecture: Electric Charge and Electric Field

Lesson Objectives - the students should be able to:

  • State from memory the magnitude and sign of the charge on an electron and proton and also state the mass of each particle.
  • Apply Coulomb's law to determine the magnitude of the electrical force between point charges separated by a distance r and state whether the force will be one of attraction or repulsion.
  • State from memory the law of conservation of charge.
  • Distinguish between an insulator, a conductor, and a semi conductor and give examples of each.
  • Explain the concept of electric field and determine the resultant electric field at a point some distance from two or more point charges.
  • Determine the magnitude and direction of the electric force on a charged particle placed in an electric field.
  • Sketch the electric field pattern in the region between charged objects.
  • Use Gauss's law to determine the magnitude of the electric field in problems where static electric charge is distributed on a surface which is simple and symmetrical.
  • Could understand Static Electricity; Electric Charge and Its Conservation
  • Solving Problems Involving Coulomb’s Law and Vectors
  • Learn Electric Forces in Molecular Biology: DNA Structure and Replication
  • Understand Photocopy Machines and Computer Printers Use Electrostatics

Lecture on Electric Charge and Electric Field PPT


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Summary of Chapter 16

  • Two kinds of electric charge – positive and negative
  • Charge is conserved
  • Charge on electron:
    Charge on electron
  • Conductors: electrons free to move
  • Insulators: nonconductors
  • Charge is quantized in units of e
  • Objects can be charged by conduction or induction
  • Coulomb’s law:
    Coulomb’s law
  • Electric field is force per unit charge:
    Electric field Formula
  • Electric field of a point charge:
    Electric field of a point charge
  • Electric field can be represented by electric field lines
  • Static electric field inside conductor is zero; surface field is perpendicular to surface
  • Electric flux:
    Electric flux formula
  • Gauss’s law:
    Gauss’s law

Units of Chapter 16 - Keywords

  • Static Electricity; Electric Charge and Its Conservation
  • Electric Charge in the Atom
  • Insulators and Conductors
  • Induced Charge; the Electroscope
  • Coulomb’s Law
  • Solving Problems Involving Coulomb’s Law and Vectors
  • The Electric Field
  • Field Lines
  • Electric Fields and Conductors
  • Gauss’s Law
  • Electric Forces in Molecular Biology: DNA Structure and Replication
  • Photocopy Machines and Computer Printers Use Electrostatics

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credit: Giancoli Physics©2013 www.FroydWess.com

Sunday, August 11, 2013

Applied Physics Lecture: The Laws of Thermodynamics

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The Laws of Thermodynamics

Lesson Objectives - the students should be able to:

  • Explain what is meant by a physical system and distinguish between an open system and a closed system.
  • State the first law of thermodynamics and use this law to solve problems.
  • Distinguish between an isothermal process, isobaric process, isochoric process and adiabatic process and draw a PV diagram for each process.
  • Calculate the work done by a gas from a PV diagram. Use the equations for an ideal gas and for the internal energy of a gas to calculate the change in internal energy of a gas and the heat added or removed during a thermodynamic process.
  • Calculate the amount of heat which must be added or removed to change the temperature of a gas held in a closed container under conditions of constant volume or constant pressure.
  • Write from memory and explain the meaning of three equivalent ways of stating the second law of thermodynamics.
  • Use the first and second laws of thermodynamics to solve problems involving a Carnot engine.
  • Distinguish between a reversible process and an irreversible process. Give examples of each type of process.
  • Determine the change in entropy for a system in which the thermodynamic process is either reversible or irreversible.
  • Distinguish between macrostate and microstate and solve problems involving the statistical interpretation of entropy.

Lecture on The Laws of Thermodynamics PPT

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Summary of Chapter 15

  • First law of thermodynamics:
    First law of thermodynamics Formula
  • Isothermal process: temperature is constant.
  • Adiabatic process: no heat is exchanged.
  • Work done by gas at constant pressure:
    Work done by gas Formula
  • Heat engine changes heat into useful work; needs temperature difference.
  • Efficiency of a heat engine:
    Efficiency of a heat engine Formula
  • Upper limit on efficiency:
    Upper limit on efficiency Formula
  • Refrigerators and air conditioners do work to extract heat from a cooler region and send it to a warmer region:
    Refrigerators and air conditioners do work
  • A heat pump is similar:
    heat pump Formula
  • Second law of thermodynamics:
    • heat flows spontaneously from a hot object to a cold one, but not the reverse
    • a given amount of heat cannot be changed entirely to work
    • natural processes tend to increase entropy.
  • Change in entropy:
    Change in entropy Formula
  • Entropy is a measure of disorder.
  • As time goes on, less and less energy is available to do useful work.

Units of Chapter 15 - Keywords

  • The First Law of Thermodynamics
  • Thermodynamic Processes and the First Law
  • Human Metabolism and the First Law
  • The Second Law of Thermodynamics – Introduction
  • Heat Engines
  • Refrigerators, Air Conditioners, and Heat Pumps
  • Entropy and the Second Law of Thermodynamics
  • Order to Disorder
  • Unavailability of Energy; Heat Death
  • Evolution and Growth; “Time’s Arrow”
  • Statistical Interpretation of Entropy and the Second Law
  • Thermal Pollution and Global Warming

Download Lecture Handout


credit: Giancoli Physics©2013 www.FroydWess.com

Friday, August 9, 2013

Applied Physics Lecture: Heat

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Applied Physics Lecture: Heat

Lesson Objectives - the students should be able to:

  • Convert from joules to calories and kilocalories and vice versa.
  • Distinguish between the concepts of temperature and heat.
  • Explain what is meant by specific heat, latent heat of fusion, and latent heat of vaporization.
  • Apply the law of conservation of energy to problems involving calorimetry.
  • Distinguish the three ways that heat transfer occurs: conduction, convection, and radiation.
  • Solve problems involving the rate of heat transfer by convection and radiation.

Lecture on Heat PPT

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Summary of Chapter 14

  • Internal energy U refers to the total energy of all molecules in an object. For an ideal monatomic gas,
    Ideal gas law Formula
  • Heat is the transfer of energy from one object to another due to a temperature difference. Heat can be measured in joules or in calories.
  • Specific heat of a substance is the energy required to change the temperature of a fixed amount of matter by 1° C.
  • In an isolated system, heat gained by one part of the system must be lost by another.
  • Calorimetry measures heat exchange quantitatively.
  • Phase changes require energy even though the temperature does not change.
  • Heat of fusion: amount of energy required to melt 1 kg of material.
  • Heat of vaporization: amount of energy required to change 1 kg of material from liquid to vapor.
  • Heat transfer takes place by conduction, convection, and radiation.
  • In conduction, energy is transferred through the collisions of molecules in the substance.
  • In convection, bulk quantities of the substance flow to areas of different temperature.
  • Radiation is the transfer of energy by electromagnetic waves.

Units of Chapter 14 - Keywords

  • Heat As Energy Transfer
  • Internal Energy
  • Specific Heat
  • Calorimetry – Solving Problems
  • Latent Heat
  • Heat Transfer: Conduction
  • Heat Transfer: Convection
  • Heat Transfer: Radiation

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credit: Giancoli Physics©2013 www.FroydWess.com
 

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