Chapter 16 Lecture

Chapter 16 A Macroscopic Description of Matter Chapter Goal: To learn the characteristics of macroscopic systems. Slide 16-2

Chapter 16 Preview Slide 16-3

Chapter 16 Preview Slide 16-4

Chapter 16 Preview Slide 16-5

Chapter 16 Preview Slide 16-6

Chapter 16 Preview Slide 16-7

Chapter 16 Reading Quiz Slide 16-8

Reading Question 16.1 What is the SI unit of pressure? The Nm2 (Newton-meter-squared). The atmosphere. The p.s.i. The Pascal. The Archimedes. Answer: D Slide 16-9 9

Reading Question 16.1 What is the SI unit of pressure? The Nm2 (Newton-meter-squared). The atmosphere. The p.s.i. The Pascal. The Archimedes. Answer: D Slide 16-10 10

Reading Question 16.2 One “mole” of monatomic helium means 0.012 kg of helium. One helium atom. One kg of helium. 4 helium atoms. 6.02  1023 helium atoms. Answer: E Slide 16-11 11

Reading Question 16.2 One “mole” of monatomic helium means 0.012 kg of helium. One helium atom. One kg of helium. 4 helium atoms. 6.02  1023 helium atoms. Answer: E Slide 16-12 12

Reading Question 16.3 The SI unit for absolute temperature is Celsius. Fahrenheit. Kelvin. Newton. Rankine. Answer: C Slide 16-13 13

Reading Question 16.3 The SI unit for absolute temperature is Celsius. Fahrenheit. Kelvin. Newton. Rankine. Answer: C Slide 16-14 14

Reading Question 16.4 The ideal-gas model is valid if The gas density and temperature are both low. The gas density and temperature are both high. The gas density is low and the temperature  is high. The gas density is high and the temperature  is low. Answer: C Slide 16-15 15

Reading Question 16.4 The ideal-gas model is valid if The gas density and temperature are both low. The gas density and temperature are both high. The gas density is low and the temperature  is high. The gas density is high and the temperature  is low. Answer: C Slide 16-16 16

Reading Question 16.5 An ideal-gas process in which the volume doesn’t change is called Isobaric. Isothermal. Isochoric. Isentropic. Answer: C Slide 16-17 17

Reading Question 16.5 An ideal-gas process in which the volume doesn’t change is called Isobaric. Isothermal. Isochoric. Isentropic. Answer: C Slide 16-18 18

Chapter 16 Content, Examples, and QuickCheck Questions Slide 16-19

Solids, Liquids, and Gases A solid is a rigid macroscopic system consisting of particle-like atoms connected by spring-like molecular bonds. Each atom vibrates around an equilibrium position but otherwise has a fixed position. Slide 16-20

Solids, Liquids, and Gases A liquid is nearly incompressible, meaning the molecules are about as close together as they can get. A liquid flows and deforms to fit the shape of its container, which tells us that the molecules are free to move around. Slide 16-21

Solids, Liquids, and Gases A gas is a system in which each molecule moves through space as a free, noninteracting particle until, on occasion, it collides with another molecule or with the wall of the container. A gas is a fluid, and it is highly compressible. Slide 16-22

Density The ratio of an object’s or material’s mass to its volume is called the mass density, or sometimes simply “the density.” The SI units of mass density are kg/m3. In this chapter we’ll use an uppercase M for the system mass and lowercase m for the mass of an atom. Slide 16-23

Densities of Various Materials Slide 16-24

Example 16.1 The Mass of a Lead Pipe Slide 16-25

Number Density It is often useful to know the number of atoms or molecules per cubic meter in a system. We call this quantity the number density. In an N-atom system that fills volume V, the number density is: The SI units of number density are m3. Slide 16-26

QuickCheck 16.1 The volume of this cube is 8 m3. 8  10–2 m3. Slide 16-27 27

QuickCheck 16.1 The volume of this cube is 8 m3. 8  10–2 m3. Slide 16-28 28

Atomic Mass and Atomic Mass Number The mass of an atom is determined primarily by its most massive constituents: protons and neutrons in its nucleus. The sum of the number of protons and neutrons is called the atomic mass number:   number of protons  number of neutrons The atomic mass, in u, is close, but not exactly, equal to the atomic mass number. u is the atomic mass unit: 1 u  1.66  1027 kg Slide 16-29

Moles and Molar Mass By definition, one mole of matter, be it solid, liquid, or gas, is the amount of substance containing Avogadro’s number NA of particles NA  6.02  1023 mol1. The number of moles in a substance containing N basic particles is One mole of helium, sulfur, copper, and mercury. Slide 16-30

Moles and Molar Mass If the atomic mass m is specified in kilograms, the number of atoms in a system of mass M can be found from: The molar mass of a substance is the mass of 1 mol of substance. The molar mass, which we’ll designate Mmol, has units kg/mol. The number of moles in a system of mass M consisting of atoms or molecules with molar mass Mmol is: Slide 16-31

QuickCheck 16.2 Which contains more molecules, a mole of hydrogen gas (H2) or a mole of oxygen gas (O2)? The hydrogen. The oxygen. They each contain the same number of molecules. Can’t tell without knowing their temperatures. Slide 16-32 32

QuickCheck 16.2 Which contains more molecules, a mole of hydrogen gas (H2) or a mole of oxygen gas (O2)? The hydrogen. The oxygen. They each contain the same number of molecules. Can’t tell without knowing their temperatures. Slide 16-33 33

Example 16.2 Moles of Oxygen Slide 16-34

Temperature What is temperature? Temperature is related to how much thermal energy is in a system (more on this in Chapter 18). For now, in a very practical sense, temperature is what we measure with a thermometer! In a glass-tube thermometer, such as the ones shown, a small volume of liquid expands or contracts when placed in contact with a “hot” or “cold” object. The object’s temperature is determined by the length of the column of liquid. Slide 16-35

Temperature The Celsius temperature scale is defined by setting TC  0 for the freezing point of pure water, and TC  100 for the boiling point. The Kelvin temperature scale has the same unit size as Celsius, with the zero point at absolute zero. The conversion from the Celsius scale to the Kelvin scale is: The Fahrenheit scale, still widely used in the United States, is defined by its relation to the Celsius scale, as follows: Slide 16-36

Temperature Slide 16-37

QuickCheck 16.3 Which is the largest increase of temperature? An increase of 1F. An increase of 1C. An increase of 1 K. Both B and C, which are the same and larger than A. A, B, and C are all the same increase. Slide 16-38 38

QuickCheck 16.3 Which is the largest increase of temperature? An increase of 1F. An increase of 1C. An increase of 1 K. Both B and C, which are the same and larger than A. A, B, and C are all the same increase. Slide 16-39 39

Absolute Zero and Absolute Temperature Figure (a) shows a constant- volume gas thermometer. Figure (b) shows the pressure-temperature relationship for three different gases. There is a linear relationship between temperature and pressure. All gases extrapolate to zero pressure at the same temperature: T0  273C. This is called absolute zero, and forms the basis for the absolute temperature scale (Kelvin). Slide 16-40

Phase Changes Suppose you were to remove an ice cube from the freezer, initially at 20C, and then warm it by transferring heat at a constant rate. Figure (b) shows the temperature as a function of time. During the phase changes of melting then boiling, energy is being added to break molecular bonds, but the temperature remains constant. Slide 16-41

Phase Changes A phase diagram is used to show how the phases and phase changes of a substance vary with both temperature and pressure. At the normal 1 atm of pressure, water crosses the solid-liquid boundary at 0C and the liquid-gas boundary at 100C. At high altitudes, where p  1 atm, water freezes at slightly above 0C and boils at a temperature below 100C. In a pressure cooker, p  1 atm and the temperature of boiling water is higher, allowing the food to cook faster. Slide 16-42

Phase Changes Food takes longer to cook at high altitudes because the boiling point of water is less than 100 C. Slide 16-43

QuickCheck 16.4 If the pressure of liquid water is suddenly decreased, it is possible that the water will Freeze. Condense. Boil. Either A or B. Either A or C. Slide 16-44 44

QuickCheck 16.4 If the pressure of liquid water is suddenly decreased, it is possible that the water will Freeze. Condense. Boil. Either A or B. Either A or C. Slide 16-45 45

Ideal Gases The ideal-gas model is one in which we model atoms in a gas as being hard spheres. Such hard spheres fly through space and occasionally interact by bouncing off each other in perfectly elastic collisions. Experiments show that the ideal-gas model is quite good for gases if two conditions are met: The density is low (i.e., the atoms occupy a volume much smaller than that of the container), and The temperature is well above the condensation point. Slide 16-46

The Ideal-Gas Law The pressure p, the volume V, the number of moles n and the temperature T of an ideal gas are related by the ideal-gas law as follows: where R is the universal gas constant, R  8.31 J/mol K. Or: where N is the number of molecules and kB is Boltzman’s constant, kB  1.38  1023 J/K. Slide 16-47

QuickCheck 16.5 If the volume of a sealed container of gas is decreased, the gas temperature Increases. Stays the same. Decreases. Not enough information to tell. Slide 16-48 48

QuickCheck 16.5 If the volume of a sealed container of gas is decreased, the gas temperature Increases. Stays the same. Decreases. Not enough information to tell. Slide 16-49 49

QuickCheck 16.6 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? TA  TB TA  TB TA  TB Not enough information to make a comparison. Slide 16-50 50

QuickCheck 16.6 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? TA  TB TA  TB TA  TB Not enough information to make a comparison. Slide 16-51 51

QuickCheck 16.7 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? pA  4pB pA  2pB pA  pB pA  pB 1 2 1 4 Slide 16-52 52

QuickCheck 16.7 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? pA  4pB pA  2pB pA  pB pA  pB 1 2 1 4 Slide 16-53 53

Example 16.3 Calculating a Gas Pressure Slide 16-54

Ideal Gases All ideal-gas problems involve a gas in a sealed container. The number of moles (and number of molecules) will not change during a problem. In that case, If the gas is initially in state i, characterized by the state variables pi, Vi, and Ti, and at some later time in a final state f, the state variables for these two states are related by: Slide 16-55

QuickCheck 16.8 The temperature of a rigid (i.e., constant-volume), sealed container of gas increases from 100C to 200C. The gas pressure increases by a factor of 2. 1.3. 1 (the pressure doesn’t change). 0.8. 0.5. Slide 16-56 56

QuickCheck 16.8 The temperature of a rigid (i.e., constant-volume), sealed container of gas increases from 100C to 200C. The gas pressure increases by a factor of 2. 1.3. 1 (the pressure doesn’t change). 0.8. 0.5. Temperatures MUST be in K, not C, to use the ideal-gas law. Slide 16-57 57

Example 16.4 Calculating a Gas Temperature Slide 16-58

Ideal-Gas Processes An ideal-gas process can be represented on a graph of pressure versus volume, called a pV diagram. Knowing p and V, and assuming that n is known for a sealed container, we can find the temperature T by using the ideal-gas law. Here is a pV diagram showing three states of a system consisting of 1 mol of gas. Slide 16-59

Ideal-Gas Processes There are infinitely many ways to change the gas from state 1 to state 3. Here are two different trajectories on the pV diagram showing how the gas might be changed from state 1 to state 3. Slide 16-60

Ideal-Gas Processes (a) If you slowly pull a piston out, you can reverse the process by slowly pushing the piston in. This is called a quasi-static process. (b) is a sudden process, which cannot be represented on a pV diagram. This textbook will always assume that processes are quasi-static. Slide 16-61

Constant-Volume Process A constant-volume process is called an isochoric process. Consider the gas in a closed, rigid container. Warming the gas with a flame will raise its pressure without changing its volume. Slide 16-62

Example 16.6 A Constant-Volume Gas Thermometer Slide 16-63

Example 16.6 A Constant-Volume Gas Thermometer Slide 16-64

Constant-Pressure Process A constant-pressure process is called an isobaric process. Consider a cylinder of gas with a tight-fitting piston of mass M that can slide up and down but seals the container. In equilibrium, the gas pressure inside the cylinder is: Slide 16-65

QuickCheck 16.9 A cylinder of gas has a frictionless but tightly sealed piston of mass M. A small flame heats the cylinder, causing the piston to slowly move upward. For the gas inside the cylinder, what kind of process is this? Isochoric. Isobaric. Isothermal. Adiabatic. None of the above. Slide 16-66 66

QuickCheck 16.9 A cylinder of gas has a frictionless but tightly sealed piston of mass M. A small flame heats the cylinder, causing the piston to slowly move upward. For the gas inside the cylinder, what kind of process is this? Isochoric. Isobaric. Isothermal. Adiabatic. None of the above. Slide 16-67 67

QuickCheck 16.10 A cylinder of gas has a frictionless but tightly sealed piston of mass M. The gas temperature is increased from an initial 27C to a final 127C. What is the final-to-initial volume ratio Vf /Vi? 1.50 1.33 1.25 1.00 Not enough information to tell. Slide 16-68 68

QuickCheck 16.10 A cylinder of gas has a frictionless but tightly sealed piston of mass M. The gas temperature is increased from an initial 27C to a final 127C. What is the final-to-initial volume ratio Vf /Vi? 1.50 1.33 1.25 1.00 Not enough information to tell. Isobaric, so Vf Tf 400 K  Vf Tf 300 K Slide 16-69 69

Example 16.7 Comparing Pressure Slide 16-70

Example 16.7 Comparing Pressure Slide 16-71

Example 16.7 Comparing Pressure Slide 16-72

Constant-Temperature Process A constant-temperature process is called an isothermal process. Consider a piston being pushed down to compress a gas. Heat is transferred through the walls of the cylinder to keep T fixed, so that: The graph of p versus V for an isotherm is a hyperbola. Slide 16-73

QuickCheck 16.11 A cylinder of gas floats in a large tank of water. It has a frictionless but tightly sealed piston of mass M. Small masses are slowly placed onto the top of the piston, causing it to slowly move downward. For the gas inside the cylinder, what kind of process is this? Isochoric. Isobaric. Isothermal. Adiabatic. None of the above. Slide 16-74 74

QuickCheck 16.11 A cylinder of gas floats in a large tank of water. It has a frictionless but tightly sealed piston of mass M. Small masses are slowly placed onto the top of the piston, causing it to slowly move downward. For the gas inside the cylinder, what kind of process is this? Isochoric. Isobaric. Isothermal. Adiabatic. None of the above. Slide 16-75 75

QuickCheck 16.12 What type of gas process is this? Isochoric. Isobaric. Isothermal. Adiabatic. None of the above. Slide 16-76 76

QuickCheck 16.12 What type of gas process is this? Isochoric. Isobaric. Isothermal. Adiabatic. None of the above. Slide 16-77 77

QuickCheck 16.13 A gas follows the process shown. What is the final-to-initial temperature ratio Tf /Ti? 2 4 8 16 Not enough information to tell. Slide 16-78 78

QuickCheck 16.13 A gas follows the process shown. What is the final-to-initial temperature ratio Tf /Ti? 2 4 8 16 Not enough information to tell. Slide 16-79 79

Example 16.10 A Multistep Process Slide 16-80

Example 16.10 A Multistep Process Slide 16-81

Example 16.10 A Multistep Process Slide 16-82

Chapter 16 Summary Slides

General Principles Slide 16-84

General Principles Slide 16-85

Important Concepts Slide 16-86

Important Concepts Slide 16-87

Important Concepts Slide 16-88