The Kinetic Theory of Gases

Transcription

1 PHYS102 Previous Exam Problems CHAPTER 19 The Kinetic Theory of Gases Ideal gas RMS speed Internal energy Isothermal process Isobaric process Isochoric process Adiabatic process General process 1. Figure 1 shows a cycle undergone by 1.0 mol of a monatomic ideal gas. What is the heat added to the gas during the whole cycle? (Ans: 520 J) 2. What is the change in the internal energy of 1.00 mole of a monatomic ideal gas that goes from point 1 (T 1 = 455K and P 1 = 1.00 atm) to point 2 (T 2 = 300 K and P 2 = 1.00 atm)? (Ans: J) mol of an ideal gas undergoes an isothermal process. The initial volume is 0.20 m 3 and the final volume is 0.30 m 3. If the heat added to the gas is 1000 J, find the temperature of the gas. (Ans: 360 K) 4. An ideal monatomic gas expands from state A to state B along the straight line path shown in figure 2. Calculate the heat absorbed by the gas in the process. (Ans: J) 5. An ideal gas is initially at a pressure of 1.40 atm and has a volume of 3.50 L. It expands isothermally to a final pressure of atm. What is the work done in the process? (Ans: J) 6. One mole of an ideal monatomic gas is taken through an adiabatic process, as shown in figure 3. Calculate the work done in this process. (Ans: 7.8 kj) 7. A gas initially at a temperature of 0 o C and a pressure of 100 kpa is compressed isothermally from 30 L to 20 L. What is the work required? (Ans: 1.2 kj) 8. An ideal monatomic gas undergoes an adiabatic expansion to one-third of its initial pressure. Find the ratio of the final volume to the initial volume. (Ans: 1.9) 9. A gas undergoes the cyclic process shown in figure 4. The net heat absorbed during the complete cycle is 1000 J. Find the work done by the gas for the process c to a. (Ans: J) 10. One mole of a monatomic ideal gas absorbs heat at constant pressure and its temperature rises from 40 o C to 90 o C. How much heat is absorbed in the process? (Ans: 1.0 kj) 11. Two moles of an ideal monatomic gas are compressed adiabatically from A to B and then further compressed isothermally from B to C, as shown in figure 5. Calculate the net heat transfer in the process from A to C. (Ans: -6.7 kj) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 19 Page 1

2 12. The pressure of an ideal monatomic gas is changed, at a constant volume of L, from atm to atm. What is the change in the internal energy of the gas? (Ans: J) 13. A sample of one mole of an ideal gas is taken through the cyclic process ABCA, as shown in figure 6. What is the net energy added to the gas as heat during the cycle? (Ans: 12 kj) 14. One mole of an ideal gas is cooled at constant pressure from 100 o C to 40 o C. Calculate the work done during the process. (Ans: 500 J) 15. A sample of argon gas (M Ar = 40 g/mole) is at four times the absolute temperature of hydrogen gas (M H = 2 g/mole). What is the ratio of the RMS speed of the argon atoms to that of hydrogen molecules? (Ans: 0.45) 16. A monatomic ideal gas is compressed adiabatically from an initial pressure of 1 atm and a volume of 800 cm 3 to a volume of 400 cm 3. If the initial temperature of the gas is 20 o C, what is the final temperature of the gas? [γ = 1.67] (Ans: 466 K) 17. An ideal gas expands at a constant pressure of 120 kpa from (a) to (b), as shown in figure 7. It is then compressed isothermally to point (c), where the volume is 40 L. Find the net work done during these two processes. (Ans: 1060 J) 18. Two moles of ideal gas are at 20 o C and a pressure of 200 kpa. If the gas is heated to 40 o C, and its pressure is reduced by 30%, what is the new volume? (Ans: 37 L) 19. An ideal monatomic gas originally in state A is taken reversibly to state B along the straight line path shown in figure 8. What is the change in the internal energy of the gas for this process? (Ans: 30 kj) 20. Five moles of an ideal gas are kept at a constant temperature of 53.0 o C while the pressure of the gas is increased from 1.00 atm to 3.00 atm. Find the work done in the process. (Ans: 14.9 kj of work done on the gas) 21. Two moles of a monatomic ideal gas, with an RMS speed, of 254 m/s are contained in a tank that has a volume of 0.15 m 3. If the molar mass of the gas is 0.39 kg/mole, what is the pressure of the gas? (Ans: Pa) 22. A cylinder of volume 2.5 L contains 0.25 moles of helium (M = 4.0 grams/mole) at 2.0 atmospheric pressure. What is the internal energy of the gas? (Ans: 0.76 kj) 23. One mole of oxygen molecules (M = 32 g/mol) occupies a cubic vessel of side length 10 cm at a temperature of 27 o C. Calculate the pressure of the gas on the walls. (Ans: Pa) 24. The equation of state of a certain gas is given as PV 2 = K, where P is the pressure, V is the volume, and K is a constant. Find the work done by the gas if its volume increases from V i = 2.0 m 3 to V f = 4.0 m 3. (Ans: K/4) 25. A diatomic ideal gas undergoes a constant pressure process in which its internal energy increases by 540 J. Find the heat added to the gas and the work done by the gas. (Ans: Q = 756 J, W = 216 J) 26. Two moles of nitrogen are in a 3-liter container at a pressure of Pa. Find the average translational kinetic energy of a molecule. (Ans: J) 27. An ideal diatomic gas (γ = 1.4), initially at pressure P i = 1.0 atm and volume V i, is allowed to expand isothermally until its volume doubles. The gas is then compressed adiabatically until it reaches its original volume. What is the final pressure of the gas? (Ans: 1.3 atm) 28. Five moles, of an ideal monatomic gas, expand at constant pressure of 100 Pa from a volume of 1.0 m 3 to a volume of 3.0 m 3. What is the change in the internal energy of the system? (Ans: 300 J) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 19 Page 2

3 29. One mole of a monatomic ideal gas at 410 K is compressed to half its original volume by an isobaric process. How much work is done in the process? (Ans: 1.7 kj done on the gas) 30. An ideal gas is allowed to expand adiabatically until its volume increases by 50 %. By what factor its initial pressure is reduced? [Assume γ = 5/3] (Ans: 2.0) 31. In an adiabatic process, the temperature of one mole of an ideal monatomic gas is decreased from 500 K to 400 K. What is the work done during the process in calories? (Ans: 300 cal) 32. For a given temperature increase, a certain amount of an ideal gas requires 80 J of heat when heated at constant volume and 150 J of heat when heated at constant pressure. How much work is done by the gas in the second situation? (Ans: + 70 J) 33. An ideal gas has an RMS speed of 254 m/s. If each gas particle has a mass of kg, what is the temperature of the gas? (Ans: 103 K) 34. Five moles of hydrogen gas occupy a balloon that is inflated to a volume of 0.3 m 3 and at 1.0 atmospheric pressure. What is the root-mean square velocity of the molecules inside the balloon? (Mass of a hydrogen atom = kg) (Ans: m/s) 35. Helium gas is heated at constant pressure from 32 o F to 212 o F. If the gas does 20.0 J of work during the process, what is the number of moles? (Ans: moles) 36. A system containing an ideal gas at a constant pressure of Pa gains 2140 J of heat. During the process, the internal energy of the system increases by 870 J. What is the change in the volume of the gas? (Ans: m 3 ) 37. One mole of an ideal gas has a temperature of 25 o C. If the volume is held constant and the pressure is doubled, what is the final temperature? (Ans: 323 o C) 38. Five moles of an ideal gas expands isothermally at 100 o C to five times its initial volume. Find the heat flow into the system. (Ans: J) 39. In the p-v diagram shown in figure 9, the ideal gas does 10 J of work when taken along the isothermal process from a to b and 8.0 J of work when taken along the adiabatic process from b to c. What is the change in internal energy of the gas when it is taken along the straight path from a to c? (Ans: J) 40. Consider 100 g of helium (He) gas at 77 K. How much heat must be supplied to the gas to increase its temperature to 24 o C, if the process is iso-volumetric? (M He = 4 g/mole and He is a monatomic gas) (Ans: 69 kj) 41. Three moles of a monatomic ideal gas at room temperature T 1 = 300K and pressure P 1 undergo an isobaric then an adiabatic expansion, as shown in figure 14. Calculate the final temperature of the gas T 3. [γ= 1.67] (Ans: 457 K) 42. An ideal gas (γ = 1.40) expands slowly and adiabatically. If the final temperature is one third the initial temperature, by what factor does the volume change? (Ans: 15.6) 43. The temperature of a gas is increased by 110 K. As result, the RMS velocity of the molecules increases from 400 m/s to 480 m/s. What is the molar mass of the gas, in g/mol? (Ans: 39) 44. Five moles of an ideal monatomic gas with an initial temperature of 127 o C expand, and in the process absorb 1200 J as heat and do 2100 J of work. What is the final temperature of the gas? (Ans: 113 C) 45. Heat flows into a monatomic gas, and the volume increases while the pressure is kept constant. What fraction of the heat energy is used to do the expansion work of the gas? (Ans: 2/5) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 19 Page 3

4 46. Two moles of an ideal monatomic gas go through the cycle shown in the p-v diagram in figure 15. For the complete cycle, 800 J of heat flows out of the gas. States A and B have temperatures T A = 200 K and T B = 300 K. What is the work during process C to A? (Ans: J) 47. The p-v diagram for a 4.3-g sample of an ideal gas contained in a container is shown in figure 16. The temperature T 1 of state 1 is 21 C. What is the temperature T 3 of state 3? (Ans: - 53 C) 48. One mole of an ideal gas is first compressed isothermally at 380 K to half of its initial volume. Then, 450 J of heat is added to it at constant volume. Find the total change in the internal energy after the gas has passed through the above two processes. (Ans: kj) 49. Two moles of a gas, originally at a pressure of 1.00 atm, occupy a volume of m 3. The gas is compressed adiabatically to half its original volume. Find the final temperature of the gas. [Use γ = 1.4] (Ans: 401 K) 50. Compute the number of molecules in 1.00 cm 3 of an ideal gas at a pressure of 100 Pa and a temperature of 20 o C. (Ans: molecules) 51. An ideal gas (γ = 1.3) is initially at V = V 1, T = 273 K, and P = 1.0 atm. The gas is compressed adiabatically to half its original volume. It is then cooled at constant pressure to its original temperature. What is the ratio of the final volume to the initial volume? (Ans: 0.4) 52. An ideal monatomic gas goes through the process shown in the T-V diagram of figure 18. At point A, the temperature is 400 K, and the volume is 2 L. If the volume at point B is 10 L, what is the temperature at point C? (Ans: 1170 K) 53. An ideal gas occupies a volume V 1 at a temperature of 100 o C. If the pressure of the gas is held constant, by what factor does the volume change when the Celsius temperature is tripled? (Ans: 1.54) 54. A 30.0 moles of an ideal gas starting at point A is carried around the cycle shown in figure 19. In the process, the gas does J of work. Find the gas temperature at point A. (Ans: 614 K) 55. A 9.0-g of helium gas undergoes the cyclic process shown figure 20. Find the work done in the process from point B C. (molar mass of helium is 4.0 g/mole) (Ans: 19 kj) 56. Two moles of hydrogen gas at o C are compressed through an isobaric process to half of the initial volume. If we assume hydrogen to be an ideal gas, what is the final RMS speed of the hydrogen molecules? [Molar mass of Hydrogen = g] (Ans: 1361 m/s) 57. As shown in the p-v diagram in figure 21, an ideal monatomic gas expands isothermally from state A to state B. The gas then cools at constant volume to state C. The gas is then compressed isobarically to state D before it is heated until it returns to state A. What is the pressure of the gas in state B? (Ans: 5 atm) 58. An ideal gas is confined in a rigid tank (constant volume) at a pressure of 12.0 atm and a temperature of 25.0 o C. If two-thirds of the gas is withdrawn and the temperature is raised to 75.0 o C, what is the pressure of the gas remaining in the tank? (Ans: 4.67 atm) 59. One mole of an ideal gas does 300 J work as it expands isothermally to a final pressure of 1.0 atm and a volume of 25 liters. Determine the initial pressure of the gas. (Ans: 1.1 atm) 60. Five moles of nitrogen are in a 5.0-liter container at a pressure of Pa. Find the average translational kinetic energy of a molecule. (Ans: J) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 19 Page 4

5 61. An ideal gas has a density of 3.75 kg/m 3, and is at a pressure of 1.00 atm. Determine the rms speed of the molecules of this gas. (Ans: 284 m/s) 62. A container having 150 kg of an ideal gas has a volume of 8.00 m 3. If the gas exerts a pressure of Pa, what is the rms speed of the molecules? (Ans: 283 m/s) 63. One mole of an ideal monatomic gas is initially at a pressure of Pa, a temperature of 300 K, and has a volume of 1.00 L. It is compressed adiabatically to a volume of L. Calculate the magnitude of the work done during this process. (Ans: 19.0 kj) 64. Four moles of a monatomic ideal gas, initially at 300 K, expand adiabatically to double the initial volume. Calculate the change in the internal energy of the gas. (Ans: 5.53 kj) 65. An ideal gas is taken from state A to state B through the process shown on the P-V diagram in figure 13. How much heat is added to the gas in this process? (Ans: J) 66. For a given temperature increase of ΔT, a certain amount of a monatomic ideal gas requires 50 J of heat when heated at constant volume, and 83 J of heat when heated at constant pressure. How much work is done by the gas in the second situation? (Ans: 33 J) 67. The temperature of an ideal gas is reduced from 100 o C to 20 o C. How much is the decrease in the rms speed of its molecules? (Ans: 11%) 68. An ideal gas has an initial temperature of 200 K, and a volume of 2.0 liters. If the volume of the gas is reduced to 1.0 liter at constant pressure, find the new average kinetic energy per molecule. (Ans: J) 69. Three moles of an ideal diatomic gas are taken through the cycle acba shown in figure 22, where cb is an adiabatic process. The temperature of the gas in states a, c, and b are T a = 300 K, T c = 492 K, and T b = 600 K, respectively. Calculate the net work for the cycle. (Ans: 1.95 kj) 70. The pressure of a monatomic ideal gas is doubled, while its volume is reduced by a factor of four. What is the ratio of the new rms speed to the initial rms speed of the atoms? (Ans: 0.71) 71. The speeds of four particles are as follows: v 1 = 1.0 m/s, v 2 = 2.0 m/s, v 3 = 3.0 m/s and v 4 = 4.0 m/s. What is their root mean square speed? (Ans: 2.7 m/s) 72. Figure 23 shows a cycle consisting of five paths: AB is isothermal at 300 K, BC is adiabatic with work = 8.0 J, CD is isobaric at 5.0 atm, DE is isothermal, and EA is adiabatic with a change of internal energy of 10 J. What is the change in the internal energy of the gas along path CD? (Ans: 2.0 J) 73. When an amount of heat of 35.1 J was added to a particular ideal gas, the volume of the gas changed from 50.0 cm 3 to 100 cm 3 while the pressure remained at 1.00 atm. If the quantity of gas present was mol, find the value of specific heats C V and C p (in J/mol.K), respectively. (Ans: 49.5 and 57.8) 74. An ideal monatomic gas is carried around the cycle ABCDA shown in figure 25. The net work done in the cycle is J. Find the heat added to the gas in process AB. (Ans: J) 75. An ideal monatomic gas, initially at pressure p i = 1.5 atm, is allowed to expand at constant pressure until its volume is doubled, as shown in figure 26. The gas is then compressed adiabatically until it reaches its initial volume. What is the final pressure of the gas? (Ans: 4.8 atm) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 19 Page 5

6 A B C D E Conceptual Problems 1. In an adiabatic process for an ideal gas, the pressure decreases. Which of the following statements is correct? A. The internal energy decreases. B. The internal energy increases. C. The internal energy remains constant. D. The work done is zero. E. The work is done on the system. 2. An ideal gas undergoes a constant-pressure process. The RMS speed A. increases as the volume increases. B. decreases as the volume increases. C. decreases as the temperature increases. D. doubles if the temperature is doubled. E. decreases by one-half if the temperature is doubled. 3. A quantity of an ideal gas is expanded to twice its initial volume. The process may be isothermal, isobaric or free expansion. Rank those three processes in order of the work done by the gas, Least to Greatest. A. Free expansion, isothermal, isobaric B. Isobaric, free expansion, isothermal C. Isothermal, isobaric, free expansion D. Isobaric, isothermal, free expansion E. Free expansion, isobaric, isothermal 4. For the cyclic process shown in figure 10: A. net thermal energy is transferred from the gas to the surroundings. B. the net work done by the gas on the surroundings is positive. C. the net work done by the gas on the surroundings is zero. D. the internal energy of the gas increases. E. the internal energy of the gas decreases. 5. Which of the following statement is incorrect? A. If the internal energy of a gas is decreased, the volume remains constant in an adiabatic process. B. In an adiabatic process, transfer of energy as heat is zero. C. The internal energy of a system increases if energy is added as heat Q for an isochoric process. D. In a cyclic process the change in internal energy of the system is zero. E. Heat energy can transfer only between bodies having different temperatures. 6. Specify the wrong statement. A. Work is a path-independent quantity. B. One mole is the number of atoms in a 12 g sample of carbon 12. C. The internal energy of an ideal gas is a function of gas temperature only. D. The internal energy is a state function. E. The kinetic theory of gasses relates the macroscopic properties of gasses to the microscopic properties of gas molecules. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 19 Page 6

7 7. If the internal energy of an ideal gas decreases by the same amount as the work done by the system, then A. the process must be adiabatic. B. the process must be isothermal. C. the process must be isobaric. D. the process must be isochoric. E. the process must be cyclic. 8. An ideal monatomic gas expands quasi-statically to twice its volume. If the process is isothermal, the work done is W i. If the process is adiabatic, the work done is W a. Which of the following statements is correct? A. 0 < Wa < Wi B. Wa = Wi C. 0 = Wa < Wi D. 0 = Wi < Wa E. 0 > Wa > Wi 9. In figure 11, paths 1 and 3 are isotherms and paths 2 and 4 are adiabatic. Which path results in the highest heat transferred to the gas? A. Path 1 B. Path 2 C. Path 3 D. Path 4 E. Paths 2 and The internal energy of a fixed mass of an ideal gas depends on: A. temperature, but not volume or pressure. B. pressure, but not volume or temperature. C. volume, but not temperature or pressure. D. temperature and pressure, but not volume. E. temperature and volume, but not pressure. 11. A mass of an ideal gas of volume V at pressure P undergoes the cyclic process shown in figure 12. At which points is the gas coolest and hottest? A. Coolest at Z and hottest at X. B. Coolest at X and hottest at Y. C. Coolest at Y and hottest at X. D. Coolest at Y and hottest at Z. E. Coolest at Z and hottest at Y. 12. Which one of the following statements is correct? A. Two different ideal gas molecules of different mass will have the same average Translational kinetic energy if they are at the same temperature. B. In an isothermal process, the work done on the gas is always positive. C. All real gases approach the ideal gas state at low temperatures. D. In an isobaric process, the energy is always constant. E. In an adiabatic process, the work is always zero. 13. Which of the following statements is correct for a gas undergoing an adiabatic process? A. There is no heat exchange between the gas and its environment. B. The internal energy of the gas is always zero. C. The pressure of the gas remains constant. D. The temperature of the gas remains constant. E. The volume of the gas remains constant. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 19 Page 7

8 14. The average translational kinetic energy of the molecules of an ideal gas in a closed, rigid container is increased by a factor of 4. What happens to the pressure of the gas? A. It increases by a factor of 4. B. It increases by a factor of 8. C. It decreases by a factor of 8. D. It remains the same. E. It decreases by a factor of A sample of an ideal gas exerts a pressure of 60 Pa when its temperature is 400 K and the number of molecules present per unit volume is n. A second sample of the same gas exerts a pressure of 30 Pa when its temperature is 300 K. How many molecules are present per unit volume of the second sample? A. 2n/3 B. 3n/2 C. n/3 D. n/2 E. 5n/3 16. Suppose one mole of an ideal gas undergoes the reversible cycle ABCA shown in figure 17, where AB is an isotherm and the temperature at point C is T c. The net heat added to the gas during the cycle is equal to 17. The temperature of an ideal gas remains constant as its volume is decreased. Which one of the following statements is correct? A. Heat flows out of the gas into the surroundings. B. The process is adiabatic. C. The pressure of the gas decreases in the process. D. The gas does positive work on its surroundings. E. The average kinetic energy of the gas molecules increases. 18. Both the pressure and volume of an ideal monatomic gas are doubled. The ratio of the new internal energy to the old internal energy is: A. 4 B. 2 C. 1 D. 1/2 E. 1/4 19. Two identical containers, one has 2.0 moles of type 1 molecules, of mass m 1, at 20 o C. The other has 2.0 moles of type 2 molecules, of mass m 2 = 2m 1, at 20 o C. What is the ratio between the average translational kinetic energy of type 2 to that of type 1? A. 1 B. 8 C. 2 D. 4 E. 16 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 19 Page 8

9 20. Which statement is incorrect? A. In an adiabatic process, the internal energy of the system always decreases. B. In a cyclic process the change in internal energy of the system is zero. C. In an adiabatic process, transfer of energy as heat is zero. D. In an isochoric process (constant volume), the internal energy of the system increases if energy is added as heat Q. E. Heat energy can be transferred only between bodies having different temperatures. 21. A sample of an ideal gas is compressed by a piston from 10 m 3 to 5 m 3 and simultaneously cooled from 540 K to 270 K. As a result there is: A. No change in pressure. B. A decrease in pressure. C. A decrease in density. D. No change in density. E. No change in volume. 22. Which of the following statements is correct? The temperature of an ideal gas decreases in A. adiabatic expansion. B. isothermal compression. C. isobaric expansion. D. adiabatic compression. E. isochoric expansion. 23. Which of the following statements is false? A. When an isolated ideal gas expands, its temperature increases. B. For an ideal gas, the specific heat at constant volume is less than the specific heat at constant pressure. C. At 400 K, the specific heat at constant volume for oxygen is equal to the specific heat at constant pressure for helium. D. The average energy per molecule of an ideal monatomic gas increases linearly with temperature. E. In an adiabatic compression, there is no heat transfer between the system and its surroundings. 24. When work is done on an ideal gas of N diatomic molecules in thermal insulation, the temperature increases by (where W is the magnitude of the work) A. 2W/5Nk B. W/3Nk C. W/2Nk D. W/Nk E. 2W/3Nk 25. The internal Energy of a certain volume of gas enclosed in a container DOES NOT depend on: A. The shape of the container B. The molecular mass of the gas C. The temperature of the gas D. The kinetic energy of the molecules of the gas E. The number of atoms in a molecule of the gas Dr. M. F. Al-Kuhaili PHYS 102 Chapter 19 Page 9

10 26. An ideal gas is held in a container of volume V at pressure P. The root mean square speed of a gas molecule under these conditions is v rms. If now the volume and pressure are changed to 2V and 2P, the root mean square speed of a molecule will be: A. 2vrms B. 4vrms C. vrms/4 D. vrms E. ½ vrms 27. Which one of the following properties of a gas is NOT consistent with the kinetic theory of gasses? A. The average speed of the gas molecules is smaller at higher temperatures. B. Gas molecules are widely separated. C. Gases fill whatever space is available to them. D. Gas molecules move rapidly in a random fashion. E. Gas molecules make elastic collisions with the walls of the container. 28. If the pressure of an ideal gas is tripled in an isothermal process, the root-mean-square speed of the molecules: A. does not change B. increases by a factor of 3 1/2 C. decreases by a factor of 3 1/2 D. increases by a factor of 2 E. decreases by a factor of An ideal gas with a volume V 0 and a pressure P 0 undergoes a free expansion to volume V 1 and pressure P 1 where V 1=32V 0. The gas is then compressed adiabatically to the original volume V 0 and pressure 4P 0. The ratio of specific heats, γ, of the ideal gas is: A. 7/5 B. 2/5 C. 3/5 D. 1/5 E. 9/5 30. An ideal gas undergoes the cyclic process shown in figure 24. What are the signs of the heats Q AB, Q BC, Q CA, respectively? A. positive, negative, negative B. positive, negative, positive C. positive, positive, negative D. negative, positive, positive E. negative, positive, negative Dr. M. F. Al-Kuhaili PHYS 102 Chapter 19 Page 10

11 Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 19 Page 11

12 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 19 Page 12