Chapter 12 - Thermal Properties of Matter w./ QuickCheck Questions

Transcription

1 Chapter 12 - Thermal Properties of Matter w./ QuickCheck Questions 2015 Pearson Education, Inc. Anastasia Ierides Department of Physics and Astronomy University of New Mexico November 3, 2015

2 Review of Last Time Isolated systems; internal & external forces; Energy - different forms (kinetic, work, etc.) Energy transformations and loss through thermal energy - from one kind of energy to another Temperature scales & thermodynamics Introduction to the atomic model

3 Basic Energy Model Work and/or heat are energy transfers that change the system s total energy If the system is isolated, the total energy is conserved

4 What is Heat? Thermodynamics is the study of thermal energy, heat, and their relationships to other forms of energy and energy transfer Heat (Q) is energy transferred between two objects due to temperature differences between them Q always flows from hot objects to cold ones

5 Thermal Energy The sum of the kinetic energy of a substance s atoms and molecules and the elastic potential energy stored in their molecular bonds is the substance s thermal energy.

6 Thermal Energy: An Atomic View Heating an ideal gas made up of N atoms, causes an increase in the energy and motion of the molecules

7 Thermal Energy: An Atomic View Heating an ideal gas made up of N atoms, causes an increase in the energy and motion of the molecules This causes an increase in the temperature

8 Thermal Energy: An Atomic View Heating an ideal gas made up of N atoms, causes an increase in the energy and motion of the molecules This causes an increase in the temperature The temperature of an ideal gas is a measure of the average kinetic energy of its atoms

9 Heat: An Atomic View Thermal energy is transferred from the faster moving atoms on the warmer side to the slower moving atoms on the cooler side

10 Heat: An Atomic View Thermal energy is transferred from the faster moving atoms on the warmer side to the slower moving atoms on the cooler side The transfer will continue until a stable situation, or thermal equilibrium, is reached

11 Temperature Scales For the Kelvin scale (units of K), zero degrees is the point at which the kinetic energy of the atoms is zero absolute zero

12 Temperature Scales For the Kelvin scale (units of K), zero degrees is the point at which the kinetic energy of the atoms is zero absolute zero All temperatures on the Kelvin scale are positive, so it is often called the absolute temperature scale

13 Temperature Scales The spacing between divisions on the Kelvin scale is the same as that on the Celsius scale

14 Temperature Scales The spacing between divisions on the Kelvin scale is the same as that on the Celsius scale Absolute zero is 273 C:

15 Temperature Scales The Celsius scale is defined so that the freezing point of water is 0 C

16 Temperature Scales The Celsius scale is defined so that the freezing point of water is 0 C The Fahrenheit scale is related to the Celsius scale:

17 Heat & Temperature Equilibrium Two systems placed in thermal contact will transfer thermal energy from hot to cold until their final temperatures are the same.

18 QuickCheck Question 11.3 Which is the largest increase of temperature? A. An increase of 1 F B. An increase of 1 C C. An increase of 1 K D. Both B and C, which are the same and larger than A E. A, B, and C are all the same increase.

19 QuickCheck Question 11.3 Which is the largest increase of temperature? A. An increase of 1 F B. An increase of 1 C C. An increase of 1 K D. Both B and C, which are the same and larger than A E. A, B, and C are all the same increase. Looking at the equations for conversion we have

20 QuickCheck Question 11.3 Which is the largest increase of temperature? A. An increase of 1 F B. An increase of 1 C C. An increase of 1 K D. Both B and C, which are the same and larger than A E. A, B, and C are all the same increase. Looking at the equations for conversion we have

21 QuickCheck Question 11.4 Which is the correct ranking of temperatures, from highest to lowest? A. 300 C > 300 K > 300 F B. 300 C > 300 F > 300 K C. 300 K > 300 F > 300 C D. 300 K > 300 C > 300 F E. 300 F > 300 K > 300 C

22 QuickCheck Question 11.4 Which is the correct ranking of temperatures, from highest to lowest? A. 300 C > 300 K > 300 F B. 300 C > 300 F > 300 K C. 300 K > 300 F > 300 C D. 300 K > 300 C > 300 F E. 300 F > 300 K > 300 C Looking, again, at the equations for conversion we have

23 QuickCheck Question 11.4 Which is the correct ranking of temperatures, from highest to lowest? A. 300 C > 300 K > 300 F B. 300 C > 300 F > 300 K C. 300 K > 300 F > 300 C D. 300 K > 300 C > 300 F E. 300 F > 300 K > 300 C T( C) = 300 K K = 27 C T( C) = 5/9 (300 F - 32 F) 149 C Looking, again, at the equations for conversion we have

24 QuickCheck Question 11.4 Which is the correct ranking of temperatures, from highest to lowest? A. 300 C > 300 K > 300 F B. 300 C > 300 F > 300 K C. 300 K > 300 F > 300 C D. 300 K > 300 C > 300 F E. 300 F > 300 K > 300 C T( C) = 300 K K = 27 C T( C) = 5/9 (300 F - 32 F) 149 C Looking, again, at the equations for conversion we have

25 QuickCheck Question 11.5 Two containers of the same gas (which we assume to be ideal) have the following masses and temperatures: Which box has the gas with the largest average kinetic energy per molecule?

26 QuickCheck Question 11.5 Two containers of the same gas (which we assume to be ideal) have the following masses and temperatures: Which box has the gas with the largest average kinetic energy per molecule? The average kinetic energy is related to the temperature of the gas on the Kelvin scale. The higher the temperature, the more average kinetic energy.

27 QuickCheck Question 11.5 Two containers of the same gas (which we assume to be ideal) have the following masses and temperatures: Which box has the gas with the largest average kinetic energy per molecule? The average kinetic energy is related to the temperature of the gas on the Kelvin scale. The higher the temperature, the more average kinetic energy.

28 QuickCheck Question 11.5 Two containers of the same gas (which we assume to be ideal) have the following masses and temperatures: T(K) = 273 K T(K) = 323 K Which box has the gas with the largest average kinetic energy per molecule? The average kinetic energy is related to the temperature of the gas on the Kelvin scale. The higher the temperature, the more average kinetic energy.

29 QuickCheck Question 11.5 Two containers of the same gas (which we assume to be ideal) have the following masses and temperatures: T(K) = 273 K T(K) = 323 K Which box has the gas with the largest average kinetic energy per molecule? The average kinetic energy is related to the temperature of the gas on the Kelvin scale. The higher the temperature, the more average kinetic energy.

30 QuickCheck Question 11.7 A steady force pushes the piston of a well-insulated cylinder in. In this process, the temperature of the gas A. Increases. B. Stays the same. C. Decreases. D. There s not enough information to tell.

31 QuickCheck Question 11.7 A steady force pushes the piston of a well-insulated cylinder in. In this process, the temperature of the gas A. Increases. B. Stays the same. C. Decreases. No heat added: Q = 0 D. There s not enough information to tell.

32 QuickCheck Question 11.7 A steady force pushes the piston of a well-insulated cylinder in. In this process, the temperature of the gas A. Increases. B. Stays the same. C. Decreases. D. There s not enough information to tell. No heat added: Q = 0 Work done on the system: W = F Δx

33 QuickCheck Question 11.7 A steady force pushes the piston of a well-insulated cylinder in. In this process, the temperature of the gas A. Increases. B. Stays the same. C. Decreases. D. There s not enough information to tell. No heat added: Q = 0 Work done on the system: W = F Δx Energy is increased!

34 QuickCheck Question 11.7 A steady force pushes the piston of a well-insulated cylinder in. In this process, the temperature of the gas A. Increases. B. Stays the same. C. Decreases. D. There s not enough information to tell. No heat added: Q = 0 Work done on the system: W = F Δx Energy is increased! Transformed to K ave

35 QuickCheck Question 11.7 A steady force pushes the piston of a well-insulated cylinder in. In this process, the temperature of the gas A. Increases. B. Stays the same. C. Decreases. D. There s not enough information to tell. The average kinetic energy is related to the temperature of the gas No heat added: Q = 0 Work done on the system: W = F Δx Energy is increased! Transformed to K ave

36 QuickCheck Question 11.7 A steady force pushes the piston of a well-insulated cylinder in. In this process, the temperature of the gas A. Increases. B. Stays the same. C. Decreases. D. There s not enough information to tell. The average kinetic energy is related to the temperature of the gas No heat added: Q = 0 Work done on the system: W = F Δx Energy is increased! Transformed to K ave

37 QuickCheck Question 11.9 A cylinder of gas has a frictionless but tightly sealed piston of mass M. Small masses are placed onto the top of the piston, causing it to slowly move downward. A water bath keeps the temperature constant. In this process A. Q > 0 B. Q = 0 C. Q < 0 D. There s not enough information to say anything about the heat.

38 QuickCheck Question 11.9 A cylinder of gas has a frictionless but tightly sealed piston of mass M. Small masses are placed onto the top of the piston, causing it to slowly move downward. A water bath keeps the temperature constant. In this process A. Q > 0 B. Q = 0 C. Q < 0 D. There s not enough information to say anything about the heat.

39 QuickCheck Question 11.9 A cylinder of gas has a frictionless but tightly sealed piston of mass M. Small masses are placed onto the top of the piston, causing it to slowly move downward. A water bath keeps the temperature constant. In this process A. Q > 0 B. Q = 0 C. Q < 0 D. There s not enough information to say anything about the heat. Work is done on the system putting energy in, but there is no change in thermal energy!

40 QuickCheck Question 11.9 A cylinder of gas has a frictionless but tightly sealed piston of mass M. Small masses are placed onto the top of the piston, causing it to slowly move downward. A water bath keeps the temperature constant. In this process A. Q > 0 B. Q = 0 C. Q < 0 D. There s not enough information to say anything about the heat. Work is done on the system putting energy in, but there is no change in thermal energy! So heat has to be taken out!

41 QuickCheck Question 11.9 A cylinder of gas has a frictionless but tightly sealed piston of mass M. Small masses are placed onto the top of the piston, causing it to slowly move downward. A water bath keeps the temperature constant. In this process A. Q > 0 B. Q = 0 C. Q < 0 D. There s not enough information to say anything about the heat. Work is done on the system putting energy in, but there is no change in thermal energy! So heat has to be taken out!

42 QuickCheck Question J is added to a sample of ideal gas as heat. The gas then expands against a piston, doing 70 J of work. During this process A. The temperature of the gas increases. B. The temperature of the gas decreases. C. The temperature of the gas stays the same.

43 QuickCheck Question J is added to a sample of ideal gas as heat. The gas then expands against a piston, doing 70 J of work. During this process A. The temperature of the gas increases. B. The temperature of the gas decreases. C. The temperature of the gas stays the same.

44 QuickCheck Question J is added to a sample of ideal gas as heat. The gas then expands against a piston, doing 70 J of work. During this process More heat is added to the system than work done by the system (energy used by the system). Thermal energy increases, causing the temperature to A. The temperature of the gas increases. B. The temperature of the gas decreases. C. The temperature of the gas stays the same.

45 QuickCheck Question J is added to a sample of ideal gas as heat. The gas then expands against a piston, doing 70 J of work. During this process More heat is added to the system than work done by the system (energy used by the system). Thermal energy increases, causing the temperature to A. The temperature of the gas increases. B. The temperature of the gas decreases. C. The temperature of the gas stays the same.

46 The 1 st Law of Thermodynamics Systems that are not moving and are not changing chemically, but whose temperatures can change, are the province of thermodynamics

47 The 1 st Law of Thermodynamics Systems that are not moving and are not changing chemically, but whose temperatures can change, are the province of thermodynamics

48 Example 11.9: Energy transfers in a blender If you mix food in a blender, the electric motor does work on the system, which consists of the food inside the container. This work can noticeably warm up the food. Suppose the blender motor runs at a power of 250 W for 40 s. During this time, 2000 J of heat flow from the now-warmer food to its cooler surroundings. By how much does the thermal energy of the food increase?

49 Example 11.9: Energy transfers in a blender PREPARE Only the thermal energy of the system changes, so we can use the first law of thermodynamics. We can find the work done by the motor from the power it generates and the time it runs.

50 Example 11.9: Energy transfers in a blender PREPARE Only the thermal energy of the system changes, so we can use the first law of thermodynamics. We can find the work done by the motor from the power it generates and the time it runs. SOLVE The work done is W = P t = (250 W)(40 s) = 10,000 J. and because heat leaves the system, its sign will be negative, so Q = 2000 J.

51 Example 11.9: Energy transfers in a blender PREPARE Only the thermal energy of the system changes, so we can use the first law of thermodynamics. We can find the work done by the motor from the power it generates and the time it runs. SOLVE The work done is W = P t = (250 W)(40 s) = 10,000 J. and because heat leaves the system, its sign will be negative, so Q = 2000 J. Then the first law of thermodynamics gives

52 Example 11.9: Energy transfers in a blender ASSESS It seems reasonable that the work done by the powerful motor rapidly increases the thermal energy, while thermal energy only slowly leaks out as heat. The increased thermal energy of the food implies an increased temperature. If you run a blender long enough, the food can actually start to steam, as the photo shows.

53 QuickCheck Question A large 20 C ice cube is dropped into a super-insulated container holding a small amount of 5 C water, then the container is sealed. Ten minutes later, is it possible that the temperature of the ice cube will be colder than 20 C? A. Yes B. No C. Maybe. It would depend on other factors.

54 QuickCheck Question A large 20 C ice cube is dropped into a super-insulated container holding a small amount of 5 C water, then the container is sealed. Ten minutes later, is it possible that the temperature of the ice cube will be colder than 20 C? A. Yes B. No C. Maybe. It would depend on other factors. Thermal equilibrium - heat travels from the hot reservoir to the colder reservoir increasing the temperature of the cold reservoir to somewhere between T H and T C.

55 QuickCheck Question A large 20 C ice cube is dropped into a super-insulated container holding a small amount of 5 C water, then the container is sealed. Ten minutes later, is it possible that the temperature of the ice cube will be colder than 20 C? A. Yes B. No C. Maybe. It would depend on other factors. Thermal equilibrium - heat travels from the hot reservoir to the colder reservoir increasing the temperature of the cold reservoir to somewhere between T H and T C.

56 Stop To Think - Review A blender does 5000 J of work on the food in its bowl. During the time the blender runs, 2000 J of heat transferred from the warm food to the cooler environment. What is the change in the thermal energy of the food? A J B J C J D J E J

57 Stop To Think - Review A blender does 5000 J of work on the food in its bowl. During the time the blender runs, 2000 J of heat transferred from the warm food to the cooler environment. What is the change in the thermal energy of the food? Invoke the first law of thermodynamics: ΔEth = W + Q A J B J C J D J E J

58 Stop To Think - Review A blender does 5000 J of work on the food in its bowl. During the time the blender runs, 2000 J of heat transferred from the warm food to the cooler environment. What is the change in the thermal energy of the food? Invoke the first law of thermodynamics: ΔEth = W + Q W = J A J B J C J D J E J

59 Stop To Think - Review A blender does 5000 J of work on the food in its bowl. During the time the blender runs, 2000 J of heat transferred from the warm food to the cooler environment. What is the change in the thermal energy of the food? Invoke the first law of thermodynamics: ΔEth = W + Q A J W = J Q = J B J C J D J E J

60 Stop To Think - Review A blender does 5000 J of work on the food in its bowl. During the time the blender runs, 2000 J of heat transferred from the warm food to the cooler environment. What is the change in the thermal energy of the food? Invoke the first law of thermodynamics: ΔEth = W + Q A J B J C J D J E J W = J Q = J ΔEth = W + Q = 5000 J + (-2000 J) = 3000 J

61 Stop To Think - Review A blender does 5000 J of work on the food in its bowl. During the time the blender runs, 2000 J of heat transferred from the warm food to the cooler environment. What is the change in the thermal energy of the food? Invoke the first law of thermodynamics: ΔEth = W + Q A J B J C J D J E J W = J Q = J ΔEth = W + Q = 5000 J + (-2000 J) = 3000 J

62 The Atomic Model of Matter We use the atomic models to illustrate the three phases of matter

63 The Atomic Model of Matter We use the atomic models to illustrate the three phases of matter

64 The Atomic Model of Matter We use the atomic models to illustrate the three phases of matter

65 The Atomic Model of Matter We use the atomic models to illustrate the three phases of matter

66 The Atomic Model of Matter In a liquid, weak bonds allow for motion while keeping the particles close together

67 The Atomic Model of Matter A gas is a system in which each particle moves freely though space until, on occasion, it collides with another particle or the wall

68 The Atomic Model of Matter A rigid solid has a definite shape and can be compressed only slightly

69 Atomic Mass and Mass Number The atomic mass number A is the sum of the number of protons and the number of neutrons in an atom. A = number of protons + number of neutrons

70 Atomic Mass and Mass Number The atomic mass number A is the sum of the number of protons and the number of neutrons in an atom. A = number of protons + number of neutrons The atomic mass scale is established by defining the mass of 21 C to be exactly 12 u

71 Atomic Mass and Mass Number The atomic mass number A is the sum of the number of protons and the number of neutrons in an atom. A = number of protons + number of neutrons The atomic mass scale is established by defining the mass of 21 C to be exactly 12 u u is the symbol for the atomic mass unit: 1 u = kg

72 Atomic Mass and Mass Number The atomic mass number A is the sum of the number of protons and the number of neutrons in an atom. A = number of protons + number of neutrons The atomic mass scale is established by defining the mass of 12 C to be exactly 12 u u is the symbol for the atomic mass unit: 1 u = kg Molecular mass is the sum of the atomic masses of the atoms that form the molecule

73 Atomic Mass and Mass Number

74 QuickCheck Question 12.1 What is the mass, in u, of a molecule of carbon dioxide, CO 2? A. 12 B. 24 C. 32 D. 36 E. 44

75 QuickCheck Question 12.1 What is the mass, in u, of a molecule of carbon dioxide, CO 2? A. 12 B. 24 C. 32 D. 36 E. 44

76 QuickCheck Question 12.1 What is the mass, in u, of a molecule of carbon dioxide, CO 2? A. 12 B. 24 C. 32 D. 36 E. 44 m(co2) = 1m( 12 C) + 2m( 16 O)

77 QuickCheck Question 12.1 What is the mass, in u, of a molecule of carbon dioxide, CO 2? A. 12 B. 24 C. 32 D. 36 E. 44 m(co2) = 1m( 12 C) + 2m( 16 O) = 1(12 u) + 2(16 u)

78 QuickCheck Question 12.1 What is the mass, in u, of a molecule of carbon dioxide, CO 2? A. 12 B. 24 C. 32 D. 36 E. 44 m(co2) = 1m( 12 C) + 2m( 16 O) = 1(12 u) + 2(16 u) = 12 u + 32 u = 44 u

79 The Definition of a Mole One way to specify the amount of substance in a system is to give its mass

80 The Definition of a Mole One way to specify the amount of substance in a system is to give its mass Another way is to measure the amount of that substance in moles 1 mole (mol) = particles

81 The Definition of a Mole One way to specify the amount of substance in a system is to give its mass Another way is to measure the amount of that substance in moles 1 mole (mol) = particles The substance is dependent on what types of molecules it is made of

82 The Definition of a Mole Monatomic gas means that the basic particles are atoms, such as helium Diatomic gas means the basic particle is a twoatom diatomic molecule, like O 2

83 QuickCheck Question 12.2 Which contains more molecules, a mole of hydrogen gas (H 2 ) or a mole of oxygen gas (O 2 )? A. The hydrogen B. The oxygen C. They each contain the same number of molecules D. Can t tell without knowing their temperatures

84 QuickCheck Question 12.2 Which contains more molecules, a mole of hydrogen gas (H 2 ) or a mole of oxygen gas (O 2 )? A. The hydrogen B. The oxygen C. They each contain the same number of molecules D. Can t tell without knowing their temperatures

85 QuickCheck Question 12.2 Which contains more molecules, a mole of hydrogen gas (H 2 ) or a mole of oxygen gas (O 2 )? A. The hydrogen B. The oxygen C. They each contain the same number of molecules D. Can t tell without knowing their temperatures

86 The Definition of a Mole The number of basic particles per mole of a substance is called Avogadro s number N A : N A = mol 1

87 The Definition of a Mole The number of basic particles per mole of a substance is called Avogadro s number NA: NA = mol 1 The number n of moles in a substance containing N basic particles is

88 The Definition of a Mole The molar mass of a substance, Mmol, is the mass in grams of 1 mol of substance:

89 Example 12.1: Determining quantities of oxygen A system contains 100 g of oxygen. How many moles does it contain? How many molecules?

90 Example 12.1: Determining quantities of oxygen A system contains 100 g of oxygen. How many moles does it contain? How many molecules? SOLVE The diatomic oxygen molecule O 2 has molar mass M mol = 32 g/mol.

91 Example 12.1: Determining quantities of oxygen A system contains 100 g of oxygen. How many moles does it contain? How many molecules? SOLVE The diatomic oxygen molecule O 2 has molar mass M mol = 32 g/mol. From

92 Example 12.1: Determining quantities of oxygen A system contains 100 g of oxygen. How many moles does it contain? How many molecules? SOLVE The diatomic oxygen molecule O 2 has molar mass M mol = 32 g/mol. From

93 Example 12.1: Determining quantities of oxygen A system contains 100 g of oxygen. How many moles does it contain? How many molecules? SOLVE The diatomic oxygen molecule O 2 has molar mass M mol = 32 g/mol. From Each mole contains N A molecules, so the total number is N = nn A = molecules.

94 QuickCheck Question 12.3 Rank the following in terms of the number of moles, from greatest number of moles to least: a. 20 g of He c. 128 g of O 2 e. 200 g of Pb b. 60 g of Ne d. 160 g of Ar A. e > d > c > b > a B. a > b > c > d > e C. a > c = d > b > e D. d > e > b = c > a E. c > a > b > e > d

95 QuickCheck Question 12.3 Rank the following in terms of the number of moles, from greatest number of moles to least: a. 20 g of He c. 128 g of O 2 e. 200 g of Pb b. 60 g of Ne d. 160 g of Ar A. e > d > c > b > a B. a > b > c > d > e C. a > c = d > b > e D. d > e > b = c > a E. c > a > b > e > d

96 QuickCheck Question 12.3 Rank the following in terms of the number of moles, from greatest number of moles to least: a. 20 g of He c. 128 g of O 2 e. 200 g of Pb b. 60 g of Ne d. 160 g of Ar A. e > d > c > b > a B. a > b > c > d > e C. a > c = d > b > e D. d > e > b = c > a E. c > a > b > e > d

97 Volume Volume V is a property that describes the amount of space a system occupies with SI units of m 3

98 Volume Volume V is a property that describes the amount of space a system occupies with SI units of m 3 It is important to note that although 1 m = 100 cm, it is not true that 1 m 3 = 100 cm 3

99 QuickCheck Question 12.4 The volume of this cube is A m 3 B. 8 m 3 C m 3 D m 3 E m 3

100 QuickCheck Question 12.4 The volume of this cube is A m 3 B. 8 m 3 C m 3 D m 3 E m m 0.02 m 0.02 m

101 QuickCheck Question 12.4 The volume of this cube is A m 3 B. 8 m 3 C m 3 D m 3 E m m 0.02 m 0.02 m V = (0.02 m) (0.02 m) (0.02 m) = m 3

102 QuickCheck Question 12.4 The volume of this cube is A m 3 B. 8 m 3 C m 3 D m 3 E m m 0.02 m 0.02 m V = (0.02 m) (0.02 m) (0.02 m) = m 3 = m 3

103 The Atomic Model of the Ideal Gas The temperature of an ideal gas is directly proportional to the average kinetic energy per atom K avg :

104 The Atomic Model of the Ideal Gas The temperature of an ideal gas is directly proportional to the average kinetic energy per atom K avg : k B is Boltzmann s constant,

105 The Atomic Model of the Ideal Gas The thermal energy of an ideal gas containing N atoms is the sum of the kinetic energies of the individual atoms:

106 The Atomic Model of the Ideal Gas The thermal energy of an ideal gas containing N atoms is the sum of the kinetic energies of the individual atoms: For an ideal gas, thermal energy is directly proportional to temperature:

107 Example 12.2: Energy needed to warm up a room A large bedroom contains about molecules of air. Estimate the energy required to raise the temperature of the air in the room by 5 C.

108 Example 12.2: Energy needed to warm up a room A large bedroom contains about molecules of air. Estimate the energy required to raise the temperature of the air in the room by 5 C. PREPARE We ll model the air as an ideal gas. The equation relates the change in thermal energy of an ideal gas to a change in temperature. The actual temperature of the gas doesn t matter only the change. The temperature increase is given as 5 C, implying a change in the absolute temperature by the same amount: T = 5 K.

109 Example 12.2: Energy needed to warm up a room SOLVE We can use to calculate the amount by which the room s thermal energy must be increased:

110 Example 12.2: Energy needed to warm up a room SOLVE We can use to calculate the amount by which the room s thermal energy must be increased:

111 Example 12.2: Energy needed to warm up a room SOLVE We can use to calculate the amount by which the room s thermal energy must be increased: This is the energy we would have to supply probably in the form of heat from a furnace to raise the temperature.

112 Example 12.2: Energy needed to warm up a room ASSESS 100 kj isn t that much energy. Table 11.2 showed it to be less than the food energy in a carrot! This seems reasonable because you know that your furnace can quickly warm up the air in a room. Heating up the walls and furnishings is another story.

113 Is it Cold in Space? The space shuttle orbits in the upper thermosphere, at about 300 km above the earth s surface. There is still a trace of atmosphere left at this altitude, and it has quite a high temperature over 1000 C.

114 Is it Cold in Space? The space shuttle orbits in the upper thermosphere, at about 300 km above the earth s surface. There is still a trace of atmosphere left at this altitude, and it has quite a high temperature over 1000 C. Although the average speed (or Kave) of the air molecules is high, there are so few air molecules present that the thermal energy is extremely low.

115 Molecular Speeds and Temperature Since temperature is proportional to the average kinetic energy of atoms, it is useful to calculate the average kinetic energy:

116 Molecular Speeds and Temperature Since temperature is proportional to the average kinetic energy of atoms, it is useful to calculate the average kinetic energy: By definition, this is the average of the squares of all the individual speeds

117 Molecular Speeds and Temperature The root-mean-square speed is the speed of an atom with the average kinetic energy. It is often referred to as the rms speed and is calculated as

118 Molecular Speeds and Temperature The root-mean-square speed is the speed of an atom with the average kinetic energy. It is often referred to as the rms speed and is calculated as From kinetic energy expression the atoms temperature (in K) can be related to their speeds as

119 Molecular Speeds and Temperature

120 Molecular Speeds and Temperature The histogram shows data from an experiment that measures the molecular speeds in nitrogen gas at 20 C

121 Molecular Speeds and Temperature The histogram shows data from an experiment that measures the molecular speeds in nitrogen gas at 20 C Almost 20% of the molecules move with the most probable speed m/s (1200 mph)

122 QuickCheck Question 12.5 A rigid container holds both hydrogen gas (H 2 ) and nitrogen gas (N 2 ) at 100 C. Which statement describes their rms speeds? A. v rms of H 2 < v rms of N 2 B. v rms of H 2 = v rms of N 2 C. v rms of H 2 > v rms of N 2

123 QuickCheck Question 12.5 A rigid container holds both hydrogen gas (H 2 ) and nitrogen gas (N 2 ) at 100 C. Which statement describes their rms speeds? A. v rms of H 2 < v rms of N 2 B. v rms of H 2 = v rms of N 2 C. v rms of H 2 > v rms of N 2

124 QuickCheck Question 12.5 A rigid container holds both hydrogen gas (H 2 ) and nitrogen gas (N 2 ) at 100 C. Which statement describes their rms speeds? A. v rms of H 2 < v rms of N 2 B. v rms of H 2 = v rms of N 2 C. v rms of H 2 > v rms of N 2

125 QuickCheck Question 12.6 An object moving faster than the earth s escape velocity (about 11 km/s) has enough energy to escape the pull of the earth s gravity. Which of the following gas molecules would be most likely to be moving at a speed high enough to escape the earth s atmosphere? A. Carbon dioxide B. Oxygen C. Nitrogen D. Water vapor E. Hydrogen

126 QuickCheck Question 12.6 An object moving faster than the earth s escape velocity (about 11 km/s) has enough energy to escape the pull of the earth s gravity. Which of the following gas molecules would be most likely to be moving at a speed high enough to escape the earth s atmosphere? A. Carbon dioxide B. Oxygen C. Nitrogen D. Water vapor E. Hydrogen

127 QuickCheck Question 12.6 An object moving faster than the earth s escape velocity (about 11 km/s) has enough energy to escape the pull of the earth s gravity. Which of the following gas molecules would be most likely to be moving at a speed high enough to escape the earth s atmosphere? A. Carbon dioxide B. Oxygen C. Nitrogen D. Water vapor E. Hydrogen

128 Example 12.3: Speed of air molecules Most of the earth s atmosphere is the gas nitrogen, which consists of molecules, N 2. At the coldest temperature ever observed on earth, 129 C, what is the root-mean-square speed of the nitrogen molecules? Does the temperature at the earth s surface ever get high enough that a typical molecule is moving at twice this speed? (The highest temperature ever observed on earth was 57 C.)

129 Example 12.3: Speed of air molecules PREPARE You can use the periodic table to determine that the mass of a nitrogen atom is 14 u. A molecule consists of two atoms, so its mass is 28 u. Thus the molecular mass in SI units (i.e., kg) is

130 Example 12.3: Speed of air molecules PREPARE You can use the periodic table to determine that the mass of a nitrogen atom is 14 u. A molecule consists of two atoms, so its mass is 28 u. Thus the molecular mass in SI units (i.e., kg) is The problem statement gives two temperatures we ll call T 1 and T 2 ; we need to express these in kelvin. The lowest temperature ever observed on earth is T 1 = = 144 K; the highest temperature is T 2 = = 330 K.

131 Example 12.3: Speed of air molecules SOLVE We use the equation for the mean square velocity to find v rms for the nitrogen molecules at T 1 :

132 Example 12.3: Speed of air molecules SOLVE We use the equation for the mean square velocity to find v rms for the nitrogen molecules at T 1 : Because the rms speed is proportional to the square root of the temperature, doubling the rms speed would require increasing the temperature by a factor of 4. The ratio of the highest temperature ever recorded to the lowest temperature ever recorded is less than this.

133 Example 12.3: Speed of air molecules SOLVE We use the equation for the mean square velocity to find v rms for the nitrogen molecules at T 1 : Because the rms speed is proportional to the square root of the temperature, doubling the rms speed would require increasing the temperature by a factor of 4. The ratio of the highest temperature ever recorded to the lowest temperature ever recorded is less than this. The temperature at the earth s surface is never high enough that nitrogen molecules move at twice the computed speed.

134 Example 12.3: Speed of air molecules ASSESS We can use the squareroot relationship to assess our computed result for the molecular speed. Figure 12.4 shows an rms speed of 510 m/s for nitrogen molecules at 20 C, or 293 K. Temperature T 1 is approximately half of this, so we d expect to compute a speed that is lower by about which is what we found.

135 Pressure - Pushing Down on Me, Pushing Down on You, No Man Asks For As particles in the gas move around in a container, they can bounce off the walls, creating a force on the walls

136 Pressure The collisions with the wall of the bicycle tire create a force perpendicular to the tire wall

137 Pressure The collisions with the wall of the bicycle tire create a force perpendicular to the tire wall If the area of the patch is doubled, then twice as many particles hit it every second

138 Pressure The pressure of the gas is the ratio of the force to the area:

139 Pressure The pressure of the gas is the ratio of the force to the area: The SI unit of pressure is the pascal, defined as

140 Pressure The pressure from the atmosphere at sea level, the standard atmosphere, is 1 standard atmosphere = 101,300 Pa 1 atm = kpa

141 Pressure The pressure from the atmosphere at sea level, the standard atmosphere, is 1 standard atmosphere = 101,300 Pa 1 atm = kpa In the U.S., pressure is often expressed in pounds per square inch, or psi: 1 atm = 14.7 psi

142 Pressure The net pressure force is exerted only where there is a pressure difference between the two sides of a surface: F net = F 2 F 1 = p 2 A p 1 A = A(p 2 p 1 ) = A Δp

143 Pressure A vacuum is an enclosed space with p << 1 atm

144 Pressure A vacuum is an enclosed space with p << 1 atm A perfect vacuum would be p = 0 Pa, but it is impossible to remove every molecule

145 Pressure A vacuum is an enclosed space with p << 1 atm A perfect vacuum would be p = 0 Pa, but it is impossible to remove every molecule The gauge pressure p g is the difference between the actual pressure and the atmospheric pressure

146 Example 12.4: Finding the force due to a pressure difference Patients suffering from decompression sickness may be treated in a hyperbaric oxygen chamber filled with oxygen at greater than atmospheric pressure. A cylindrical chamber with flat end plates of diameter 0.75 m is filled with oxygen to a gauge pressure of 27 kpa. What is the resulting force on the end plate of the cylinder?

147 Example 12.4: Finding the force due to a pressure difference Patients suffering from decompression sickness may be treated in a hyperbaric oxygen chamber filled with oxygen at greater than atmospheric pressure. A cylindrical chamber with flat end plates of diameter 0.75 m is filled with oxygen to a gauge pressure of 27 kpa. What is the resulting force on the end plate of the cylinder? PREPARE There is a force on the end plate because of the pressure difference between the inside and outside. 27 kpa is the pressure in excess of 1 atm. If we assume the pressure outside is 1 atm, then 27 kpa is p, the pressure difference across the surface.

148 Example 12.4: Finding the force due to a pressure difference SOLVE The end plate has area A = π(0.75 m/2) 2 = m 2. The pressure difference results in a net force F net = A p = (0.442 m 2 )(27,000 Pa) = 12 kn

149 Example 12.4: Finding the force due to a pressure difference SOLVE The end plate has area A = π(0.75 m/2) 2 = m 2. The pressure difference results in a net force F net = A p = (0.442 m 2 )(27,000 Pa) = 12 kn ASSESS The area of the end plate is large, so we expect a large force. Our answer makes sense, although it is remarkable to think that this force results from the collisions of individual molecules with the plate. The large pressure force must be offset with an equally large force to keep the plate in place, so the end plate is fastened with stout bolts.

150 From Collisions to Pressure and the Ideal-Gas Law Pressure should be proportional to the temperature of the gas: p T

151 From Collisions to Pressure and the Ideal-Gas Law Pressure should be proportional to the temperature of the gas: p T Pressure should be inversely proportional to the volume of the container: p 1/V

152 From Collisions to Pressure and the Ideal-Gas Law Pressure should be proportional to the temperature of the gas: p T Pressure should be inversely proportional to the volume of the container: p 1/V Pressure should be proportional to the number of gas particles: p N

153 From Collisions to Pressure and the Ideal-Gas Law The ideal-gas law relates the pressure, temperature, and volume of an ideal gas:

154 From Collisions to Pressure and the Ideal-Gas Law The ideal-gas law relates the pressure, temperature, and volume of an ideal gas: The proportionality constant R is known as the gas constant: R = N A k B = 8.31 J/mol K

155 From Collisions to Pressure and the Ideal-Gas Law Let s review the meaning and the units of the various quantities in the ideal-gas law:

156 Example 12.5 Finding the volume of a mole What volume is occupied by 1 mole of an ideal gas at a pressure of 1.00 atm and a temperature of 0 C?

157 Example 12.5 Finding the volume of a mole What volume is occupied by 1 mole of an ideal gas at a pressure of 1.00 atm and a temperature of 0 C? PREPARE The first step in ideal-gas law calculations is to convert all quantities to SI units:

158 Example 12.5 Finding the volume of a mole What volume is occupied by 1 mole of an ideal gas at a pressure of 1.00 atm and a temperature of 0 C? PREPARE The first step in ideal-gas law calculations is to convert all quantities to SI units: SOLVE We use the ideal-gas law equation to compute

159 Example 12.5 Finding the volume of a mole SOLVE We recall from earlier in the chapter that 1.00 m 3 = 1000 L, so we can write

160 Example 12.5 Finding the volume of a mole SOLVE We recall from earlier in the chapter that 1.00 m 3 = 1000 L, so we can write ASSESS At this temperature and pressure, we find that the volume of 1 mole of a gas is 22.4 L, a result you might recall from chemistry. When we do calculations using gases, it will be useful to keep this volume in mind to see if our answers make physical sense.

161 QuickCheck Question 12.8 The two identical cylinders each have lightweight pistons on top that are free to move, so the pressure inside each cylinder is equal to atmospheric pressure. One cylinder contains H 2 N 2 Same volumes hydrogen, the other nitrogen. Both gases are at the same temperature. The number of moles of hydrogen is A. Greater than the number of moles of nitrogen. B. Equal to the number of moles of nitrogen. C. Less than the number of moles of nitrogen.

162 QuickCheck Question 12.8 The two identical cylinders each have lightweight pistons on top that are free to move, so the pressure inside each cylinder is equal to atmospheric pressure. One cylinder contains H 2 N 2 Same volumes hydrogen, the other nitrogen. Both gases are at the same temperature. The number of moles of hydrogen is A. Greater than the number of moles of nitrogen. B. Equal to the number of moles of nitrogen. C. Less than the number of moles of nitrogen.

163 QuickCheck Question 12.8 The two identical cylinders each have lightweight pistons on top that are free to move, so the pressure inside each cylinder is equal to atmospheric pressure. One cylinder contains H 2 N 2 Same volumes hydrogen, the other nitrogen. Both gases are at the same temperature. The number of moles of hydrogen is A. Greater than the number of moles of nitrogen. B. Equal to the number of moles of nitrogen. C. Less than the number of moles of nitrogen.

164 QuickCheck Question 12.8 The two identical cylinders each have lightweight pistons on top that are free to move, so the pressure inside each cylinder is equal to atmospheric pressure. One cylinder contains H 2 N 2 Same volumes hydrogen, the other nitrogen. Both gases are at the same temperature. The number of moles of hydrogen is A. Greater than the number of moles of nitrogen. B. Equal to the number of moles of nitrogen. C. Less than the number of moles of nitrogen.

165 QuickCheck Question 12.9 The two identical cylinders each have lightweight pistons on top that are free to move, so the pressure inside each cylinder is equal to atmospheric pressure. One cylinder contains hydrogen, the other nitrogen. The mass of gas in each cylinder is the same. The temperature of the hydrogen gas is H 2 N 2 Same volumes A. Greater than the temperature of the nitrogen. B. Equal to the temperature of the nitrogen. C. Less than the temperature of the nitrogen.

166 QuickCheck Question 12.9 The two identical cylinders each have lightweight pistons on top that are free to move, so the pressure inside each cylinder is equal to atmospheric pressure. One cylinder contains hydrogen, the other nitrogen. The mass of gas in each cylinder is the same. The temperature of the hydrogen gas is H 2 N 2 Same volumes A. Greater than the temperature of the nitrogen. B. Equal to the temperature of the nitrogen. C. Less than the temperature of the nitrogen.

167 QuickCheck Question 12.9 The two identical cylinders each have lightweight pistons on top that are free to move, so the pressure inside each cylinder is equal to atmospheric pressure. One cylinder contains hydrogen, the other nitrogen. The mass of gas in each cylinder is the same. The temperature of the hydrogen gas is H 2 N 2 Same volumes A. Greater than the temperature of the nitrogen. B. Equal to the temperature of the nitrogen. C. Less than the temperature of the nitrogen.

168 QuickCheck Question Two identical cylinders, A and B, contain the same type of gas at the same pressure. Cylinder A has twice as much gas as cylinder B. Which is true? A. T A < T B B. T A = T B C. T A > T B D. Not enough information to make a comparison

169 QuickCheck Question Two identical cylinders, A and B, contain the same type of gas at the same pressure. Cylinder A has twice as much gas as cylinder B. Which is true? A. T A < T B B. T A = T B C. T A > T B D. Not enough information to make a comparison

170 QuickCheck Question Two identical cylinders, A and B, contain the same type of gas at the same pressure. Cylinder A has twice as much gas as cylinder B. Which is true? A. T A < T B B. T A = T B C. T A > T B D. Not enough information to make a comparison

171 QuickCheck Question Two cylinders, A and B, contain the same type of gas at the same temperature. Cylinder A has twice the volume as cylinder B and contains half as many molecules as cylinder B. Which is true? A. p A = 4p B B. p A = 2p B C. p A = p B D. p A = ½ p B E. p A = ¼ p B

172 QuickCheck Question Two cylinders, A and B, contain the same type of gas at the same temperature. Cylinder A has twice the volume as cylinder B and contains half as many molecules as cylinder B. Which is true? A. p A = 4p B B. p A = 2p B C. p A = p B D. p A = ½ p B E. p A = ¼ p B

173 QuickCheck Question Two cylinders, A and B, contain the same type of gas at the same temperature. Cylinder A has twice the volume as cylinder B and contains half as many molecules as cylinder B. Which is true? A. p A = 4p B B. p A = 2p B C. p A = p B D. p A = ½ p B E. p A = ¼ p B

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184 Things that are due Homework #8 Due November 2, 2015 by 11:59 pm Reading Quiz #12 Due November 5, 2015 by 4:59 pm Reading Quiz #13 Due November 10, 2015 by 4:59 pm

185 QUESTIONS?