1. Energy Glenn V. Lo Department of Physical Sciences Nicholls State University

2. Energy Energy is an important property of matter Energy is related to the motion of atoms and molecules Understanding energy helps us understand behavior of atoms and molecules

3. Position Vector Position is an example of a vector: something that is defined by specifying magnitude and direction. To locate something, specify a reference point (the “origin”). how far it is from the origin? direction to take to get there? For object moving on a straight line, pick any point on the line as the origin. if location is “x”, and d is the distance from the origin then  x=+d if object is one side,  x=-d if object is on the other side  Choice of + and – directions is arbitrary Example: If x=+5.0 m is 5.0 meters to the right of the origin, then x=-4.0 m is…

4. Displacement vector,  x Change in location For 1-dimensional motion,  x  x = x 2 – x 1 where x 2 = location at time t 2 x 1 = location at time t 1 Example: An object moves 3.0 meters to the left. What is the displacement?

5. Distance traveled If object does not change direction, distance traveled is the absolute value of the displacement: d = |  x|. Example: An object moves 2.0 m to the right, then 3.0 m to the left. Calculate the displacements for each leg and the total distance traveled.

6. Speed How fast an object is moving Average speed = distance traveled, divided by elapsed time Example: Suppose an object travels 10.0 m in 2.0 min. Calculate its average speed? Why “average”?

7. Velocity Velocity is a vector. At any given instant, the magnitude of the velocity is the speed. the direction is specified by using (+) values if object is moving one way and (-) value if it is moving in the opposite direction. Choice of (+) and (-) directions is arbitrary Example: An object is moving with a velocity of -5.0 m/s. What is its speed? Which direction?

8. Acceleration If velocity is changing, object is said to be accelerating. Average acceleration =  v /  t Unit for a is m/s/s, or m s -2 True or False. An object moving at constant speed is not accelerating.

9. Example: speeding up Acceleration and velocity have the same algebraic sign An object moving in a straight line speeds up from 4.0 m s -1 to 8.0 m s -1 in 4.0 s. Calculate the average acceleration.

10. Example: slowing down Acceleration and velocity have opposite algebraic signs An object moving in a straight line slows down from -4.0 m s -1 to -2.0 m s -1 in 2.0 s. Calculate the average acceleration.

11. Example: changing direction If an object reverses direction, a and the original v have opposite signs. A molecule moving at 500.0 m s -1 towards a wall, collides with the wall, then moves in the opposite direction at a constant speed of 500.0 m s -1 during a time interval of 0.10 s. Calculate the average acceleration during this time interval?

12. Force A push or pull Force is a vector. For 1-D motion: force is (+) in one direction, (-) in the opposite sum of all forces = “net force” SI unit of force: newton (N). 1 N = 1 kg m s -2 Newton’s Laws explain observed motion in terms of forces: 1st Law: natural tendency of objects is to move at constant velocity 2 nd Law: F = ma, where m=mass, a=acceleration. An object speeds up of slows down subjected to “unbalanced” forces 3 rd Law: for every action there is an equal and opposite reaction. If object 1 exerts a force on object 2, then object 2 exerts an equal force on object 1 in the opposite direction.

13. Example A force of 5 N pushes a object to the right. A force of 7 N pulls it to the left. What is the net force on the object?

14. Newton’s 2 nd Law Newton’s 2 nd Law: F = ma where m = mass and a = acceleration Which will experience a greater acceleration if subjected to the same net force, a proton or an electron?

15. Direction of force Since: F = ma F and a vectors are always pointing in the same direction. Their algebraic sign is the same. If an object speeds up in a given direction, it is experiencing a push or pull in that direction. If an object slows down in a given direction, it is experiencing a push or pull in the opposite direction Example: An object heading east slows down. What is the direction of the force?

16. Example The speed of a 10.0 kg object in “free fall” increases by 9.8 m/s every second. Calculate the force on the object.

17. Weight For objects near the earth’s surface, acceleration due to the earth’s pull (the force of gravity) gravity is g = 9.8 m s -2. The magnitude of the force of gravity is called weight: W = mg What is the weight of 0.50 kg book? How much force does the book exert on the earth?

18. Air resistance An object’s downward acceleration near the surface of the earth may be significantly less than 9.8 m s -2. Why?

19. Normal Force Normal force = due to objects in contact Example: A 10.0 kg book is at rest on a table. What is the force of gravity on the book? What is the net force? What is the upward force? What is responsible for the upward force?

20. Frictional Force Any type of force the retards motion. Suppose we attempt to push a book to the right with a 10.0N force but it doesn’t move. What is the frictional force? What is responsible for this force?

21. Fundamental Forces Forces in nature can be classified into four fundamental types: gravitational, electromagnetic, strong, and weak. Strong and weak forces significant only at very, very short distances (like between protons and neutrons in an atom’s nucleus). Gravitational force: depends on masses of objects and distance between them. Electromagnetic force: affects charged particles only. Interaction of atoms and molecules are mainly due to electromagnetic forces among electrons and nuclei.

22. Gravitational and Electromagnetic Gravitational force: exists between any pair of particles, depends on masses of particles and square of distance between them: F = G m 1 m 2 / r 2 where G = 6.67x10 -11 N kg -2 m 2 Electromagnetic: Coulombic or electrostatic force: exists between any pair of charged particles.  Depends on distance between the particles (Coulomb’s Law). F = k q 1 q 2 / r 2 where k = 9.0x10 9 N C -2 m 2 Magnetic force: generated by movement of charged particles; affects moving charged particles. Protons and electrons also have intrinsic magnetism.

23. Example In a hydrogen atom, most probable distance between proton and electron is 52.9 pm. Compare gravitational force between them to the Coulombic force. m p = 1.67x10 -27 kg, m e = 9.11x10 -31 kg q p = +1.602x10 -19 C, q e = -1.602x10 -19 C F grav = 3.63x10 -47 N F coul = 8.25x10 -8 N

24. Test Yourself An object is speeding up as it moves in the -x direction. The net force on the object is... A. positive B. negative C. zero

25. Test Yourself When an atom moving in the +x direction collides with a wall and reverses direction, which of the following is true? A. the acceleration of the atom is negative B. the force on the atom in positive C. the force on the wall is negative

26. Test Yourself When subjected to the same amount of force, which of these atoms would experience greater acceleration? A. H B. He

27. Test Yourself At typical atomic distances, the predominant fundamental force between charged particles is... A. strong B. weak C. electromagnetic D. gravitational

28. Kinetic Energy A moving object is said to have “kinetic energy” Kinetic energy = (1/2) (mass) (speed) 2 Same object, faster speed  more K.E. Same speed, heavier object  more K.E. SI Unit: Joule (J), or kg m 2 s -2

29. Test Yourself Which has greater kinetic energy? A. A He atom moving at 300 m s -1 B. A Ne atom moving at 300 m s -1 C. neither; they have the same kinetic energy

30. Example Calculate the kinetic energy of a N 2 molecule (mass = 4.65x10 -26 kg) moving at 474 m s -1. This is the average speed of nitrogen molecules at room temperature (298K).

31. Example Energies of atoms and molecules in Joules tend to be very small. A more convenient unit to use is the electron volt (eV). Calculate the average kinetic energy in eV for N 2 molecules at room temperature?

32. Work Work = application of force over a distance work = force times displacement: w = f  x Unit of work is same as for kinetic energy, Joule (J). 1 N m = (kg m s -2 )(m) = 1 J Example: Calculate work done due to gravity when a 1.00 kg object falls a distance of 0.50 m. Assume downward direction is positive.

33. Work-Energy Theorem Work = change in kinetic energy. w =  KE Work can be positive or negative, but it is not a vector; algebraic sign does not indicate direction. Positive work  object has gained kinetic energy (sped up) Negative work  object has lost kinetic energy Example: By how much does the kinetic energy of a 1.00 kg object change when it falls a distance of 0.50 m. What is the speed at this point assuming it starts from rest?

34. Types of Kinetic Energy Translation = movement from place to place Kinetic energy associated with movement from place to place is called translational energy. In addition to translational energy, molecules have kinetic energy due to the motion of the atoms in the molecule relative to each other. This relative motion can be described as vibration and rotation. Relative KE = vibrational energy + rotational energy Unbonded atoms do not have relative KE. Watch this video: http://goo.gl/p091w (http://archive.org/details/MolecularMotionssecondEdition)

35. Test Yourself Which of the following does not have vibrational or rotational energy? A. A neon atom B. An O 2 molecule

36. Potential and Total Energy Any pair of particles is said to have a potential energy, V, due to the force they exert on each other. The force, and therefore V, depend on the distance between the particles. Thus, potential energy is defined as energy due to position. For any set of particles, the sum of all kinetic and potential energies is called the “total energy”, E. Example: Write E in terms of V and K for a set of three particles

37. Potential energy Potential energy is defined so that the total E for any set of particles, left alone, is constant. In other words, total energy of the universe is constant (the “Law of Conservation of Energy”). Can we prove? No, it’s an assumption. But it’s consistent with reality. The value of potential energy itself means nothing. It’s the change in potential energy that’s important. A drop in potential energy means… An increase in potential energy means… For calculations, it is customary to assign a value of zero for potential energy when two particles are separated at infinite distance from each other.

38. Example Describe what happens to the potential energy of an electron as it moves away from a proton?

39. Example Shown below (red curve) is the potential energy for a proton and an electron (as in a hydrogen atom). If the green line represents the total energy, describe the two particles when they are separated at distances corresponding to points A, B, and C on the graph.

40. Example Shown below (in red) is the potential energy for a proton and an electron (as in a hydrogen atom). If the green line (at 1x10 -18 J) represents the total energy, describe what happens when the particles are separated by 1000 pm..

41. Example Which curve corresponds to the potential energy between two electrons?

42. Covalent bonding in H 2 Red curve shows potential energy between two protons. Blue curve shows the potential energy of two protons in the presence of two electrons. Average (relative KE + potential energy) of H 2 molecules at room temperature is shown by green line. Describe the motion of the two protons.

43. Simulation http://goo.gl/5zvGg http://phet.colorado.edu/en/simulation/atomic-interactions

44. Example Consider the potential energy curve for H 2 shown in red. For which of the two energy levels indicated do we expect the two atoms to be able to move farther from each other?

45. Bond Energy D e = “well depth” = bond dissociation energy Atoms will separate if they gain energy equal to D e from a “third body” (another atom or molecule) by collision. When atoms are separated as a result, their relative KE remains the same but potential energy increases. Dissociation means conversion of translational energy of third body to potential energy of the separated atoms.

46. Bond Energy Bonded atoms in a molecule are said to be a deep well (D e around 10 -18 J or 5 eV) Two atoms or two molecules with very weak attraction for each other are in a shallow well (D e is less than 0.05 eV). Average translational energy of gas particles at room temperature: 0.04 eV Enough to separate two molecules apart, but not two bonded atoms (within a molecule).

47. Example Average translational energy of gas particles is (3/2)kT, where k=1.38x10 -23 J/K D e to separate two N atoms in N 2 is 1.6x10 -18 J What temperature is needed so that an average gas particle can break up N 2 molecule into two N atoms by collision? Ans: about 77000K

48. Test Yourself As two protons approach each other, their potential energy... A. increases B. decreases C. remains the same

49. Test Yourself The formation of a bond between two atoms involves a conversion of: A. potential energy to kinetic energy B. kinetic energy into potential energy

50. Test Yourself The bond dissociation energy of a diatomic molecule is 4.9x10 -19 J. If one of these molecules, with a relative kinetic energy of 1.2x10 -19 J, were to gain 5.3x10 -19 J of energy from a third body, calculate the relative kinetic energy of the separated atoms. Sketch the molecular potential energy curve.

51. Energy and Temperature “System” = anything we are interested in, like a sample of a matter. “Surroundings” = the rest of the universe Thermal energy = sum of kinetic energies of atoms in a system. Example of an “extensive” or “extrinsic” property; directly proportional to amount of sample. Temperature = “hotness”; a measure of the average kinetic energy of atoms in a system. Example of an “intensive” or “intrinsic” property; is independent of amount of sample. Heat = energy that is transferred when a system and its immediate surroundings are at different temperatures.

52. Example Consider the following: Sample A: 5.0 g Cu at 50 o C Sample B: 10.0 g of Cu at 50 o C Which sample has atoms with higher average kinetic energy? Which sample has more thermal energy? Will heat flow between samples A and B?

53. Example Consider the following: Sample A: 5.0 g Cu at 50 o C Sample B: 5.0 g of Cu at 100 o C Which sample has atoms with higher average kinetic energy? Which sample has more thermal energy? Will heat flow between samples A and B?

54. Heat and Work Transfer of energy is classified as either “heat” or “work” Heat = due to temperature difference Work = due to everything else; due to application of a force over a distance Atomic Interpretation: Heat is due to random collisions of atoms. Collisions between atoms lead to transfer of kinetic energy. Atoms are always moving. Work is due to collisions resulting from organized motion of atoms (“mechanical work”) or electrons (“electrical work”).

55. Example Which of the following ways of increasing the temperature of a nail is classified as heating? A. Putting it on a hot stove B. Hitting it with a hammer C. Passing electricity through it

56. Algebraic Signs for energy transfers If a system gains energy,  E>0 (positive) If a system loses energy,  E<0 (negative) If heat flows into a system, q > 0 (positive), process is endothermic. If heat flows out of a system, q < 0 (negative), process is exothermic. Example: a hot piece of metal cools to room temperature. What is the algebraic sign of q? Is the process endothermic or exothermic?

57. Heat capacity If there is no significant change in potential energy of atoms when energy is transferred (by heat or work), we can use the change in temperature to determine the amount of energy transferred.  E due to heat = q = C  T Larger  T means … C = q/  T = “heat capacity,” the energy needed to raise the temperature of the system by 1 o C, or 1K. Unit for C is… NOTE: Significant change in potential energy occurs when there is a significant change in distances between atoms. (either a “phase change” or a “chemical change” has occurred)

58. Specific Heat For homogeneous systems (which has uniform properties throughout), we can calculate C by looking up the the specific heat capacity (c), the “heat capacity per gram” and multiplying it by the mass in grams (m). The specific heat of water is 4.18 J K -1 g -1. What is the heat capacity of 100.0 g of water?

59. Example How much energy is transferred when 100.0 g of water at room temperature (25.0 o C) is cooled to 15.0 o C?

60. Determining heat capacity Calorimeter = an insulated container (no heat flow into our out of the container). To determine heat capacity: Mix two samples that are at different temperatures in a calorimeter Energy lost by one sample equals energy gained by other sample: C 1  T 1 + C 2  T 2 = 0 Measure  T 1 and  T 2. If you know C 1, then C 2 = - C 1  T 1 /  T 2 NOTE: James Joule showed that heat and work are just two different ways of transferring the same thing (energy). Before Joule’s work, the calorie was defined as the heat needed to raise the temperature of 1 g of water by 1 degree Celsius; in other words: c = 1 cal o C -1 g -1. Modern definition: 1 cal = 4.184 J

61. Example A piece of metal at 5.0 o C is mixed with 100.0 g of water at 25 o C in a calorimeter. The final temperature of the mixture is 15.0 o C. Calculate the heat capacity of the metal. What additional information would you need to determine the specific heat of the metal?

62. Test Yourself Passing electricity through a wire dipped in water causes the temperature of both the wire and water to increase. The temperature change in the wire is due to _______ and the temperature change in the water is due to _______. A. heat, heat, B. heat, work C. work, heat, D. work, work

63. Test Yourself A pot of water at room temperature is placed on a hot stove. If 5.0 kJ of heat is transferred, q for the pot of water is ______ and q for the stove is ______. A. +5.0 kJ, +5.0 kJ B. –5.0 kJ, -5.0 kJ C. +5.0 kJ, -5.0 kJ D. –5.0 kJ, +5.0 kJ

64. Test Yourself What is the specific heat of a substance if a 30.0 g sample has a heat capacity of 3.00 J/K? A. 0.100 J o C -1 g -1, B. 90.0 J g K -1, C. 10.0 J -1 K g

65. Test Yourself What is the specific heat of a substance if the temperature of a 35.0 g sample increases from 25.0 o C to 27.0 o C with the absorption of 14.0 J of heat? A. 0.400 J g -1, B. 7.0 J K -1, C. 0.200 J K -1 g -1

66. Test Yourself It takes 8.4x10 3 J of heat to raise the temperature of a system from 25.0 o C to 35.0 o C. What is the heat capacity of the system? A. 8.4x10 2 J K -1 B. 8.4x10 4 J/ o C C. 2.9x10 1 J/K

67. Test Yourself How much heat is needed to raise the temperature of a system from 20.0 o C to 25.0 o C if the heat capacity of the system is 8.00x10 2 J K -1 ? A. 1.60x10 2 J B. 2.22x10 5 J C. 4.0x10 3 J

68. Test Yourself What is the final temperature of an object, initially at 25.0 o C, if 5.00x10 3 J of heat flows out of it? Assume that the heat capacity is 2.50x10 3 J K -1. A.–250.0 o C, B. –2.00 o C, C. 23.0 o C, D. 27.0 o C