Advanced Physics Chapter 13 Temperature and Kinetic Theory

Chapter 13 Temperature and Kinetic Theory 13-1 Atomic Theory of Matter 13-2 Temperature and Thermometers 13-3 Thermal Equilibrium and the Zeroth Law of Thermodynamics 13-4 Thermal Expansion 13-5 Anomalous Behavior of Water Below 4  C 13-6 Thermal Stress 13-7 The Gas Laws and Absolute Temperature 13-8 The Ideal Gas Law 13-9 Solving Problems with the Ideal Gas Law Ideal Gas Law: Avogadro’s Number Kinetic Theory Distribution of Molecular Speeds Real Gases and Phase Change Vapor Pressure and Humidity Diffusion

13-1 Atomic Theory of Matter Kinetic Theory of Matter Theory that matter is made up of atoms that are in constant random straight line motion

13-1 Atomic Theory of Matter Element Atom Evidence for atomic theory: Law of Definite Proportions Brownian Motion Atomic Mass (Molecular Mass) (Unified) Atomic Mass Unit-u = 1.66 x kg

13-1 Atomic Theory of Matter Compound Molecules Formula unit Molecular (formula) mass Properties (phases) of matter: Macroscopic (shape/volume) Microscopic (intermolecular forces)

13-2 Temperature and Thermometers Temperature =???? Units of measure Measurement instruments Uses Heat = ???? Unit of measure Measurement instruments

13-3 Thermal Equilibrium and the Zeroth Law of Thermodynamics Thermal Equilibrium: When two objects that are in contact have no energy flow between them and their temperatures don’t change (heat) energy transfers from hot to cold Thermal equilibrium  E  T

13-3 Thermal Equilibrium and the Zeroth Law of Thermodynamics Thermal Equilibrium: If there are three systems in contact with each other and A and C are in thermal equilibrium B and C are in thermal equilibrium Are A and B in thermal equilibrium? A B C

13-3 Thermal Equilibrium and the Zeroth Law of Thermodynamics Zeroth Law of Thermal Equilibrium: If two systems are in thermal equilibrium with a third then they are in thermal equilibrium with each other. A B C

13-3 Thermal Equilibrium and the Zeroth Law of Thermodynamics Zeroth Law of Thermal Equilibrium: Systems that are in thermal equilibrium have the same temperature so this law provides a useful definition of temperature.

13-4 Thermal Expansion Most substances will expand when heated and contract when cooled. For most solids there is a direct proportion between the change in temperature and the increase in length or volume.

13-4 Thermal Expansion For linear expansion:  L =  L o  T where:  is the coefficient of linear expansion (p.388) for solids  is for materials at 20  C since the value changes with changing (starting) temperature. If a hole is cut in a cookie sheet and then heated, will the hole get larger or smaller?

13-4 Thermal Expansion For linear expansion:  L =  L o  T Also L = L o (1 +   T )  units C -1

13-4 Thermal Expansion For volume expansion:  V =  V o  T where:  is the coefficient of linear expansion (p.388) and is for solids, liquids and gases  is for materials at 20  C since the value changes with changing (starting) temperature. When does it cost less to fill your car with gasoline, morning or night?

13-4 Thermal Expansion For volume expansion:  V =  V o  T Also V = V o (1 +  T ) For solids   3 

13-5 Anomalous Behavior of Water Below 4  C Most substances expand more or less uniformly with an increase in temperature Water actually decreases in volume when it goes from 0  C to 4  C! Water is most dense at 4  C.

13-5 Anomalous Behavior of Water Below 4  C This increase in density is of extreme importance for life on Earth. When a lake freezes it freezes from the top down (not from bottom up like most liquids) Why?

13-5 Anomalous Behavior of Water Below 4  C Also water is more dense as a liquid than it is when it is a solid. WHY?

13-6 Thermal Stress When temperature changes large compressional or tensile stresses can occur. These stresses are called thermal stresses

13-6 Thermal Stress Thermal stress Remember…..  L = (1/E)(F/A)L o When there is a change in temperature:  L o  T = (1/E)(F/A)L o So….. F =  EA  T or Stress = F/A =  E  T E is Young’s Modulus

13-7 The Gas Laws and Absolute Temperature Equation of State Relationship between the physical conditions of a system Equilibrium States of a system Variables that describe the system are the same throughout the system and are not changing in time. Variables that describe a state of a gas are?

13-7 The Gas Laws and Absolute Temperature Boyle’s Law The volume of a gas is inversely proportional to the pressure applied if temperature is kept constant P 1 V 1 = P 2 V 2

13-7 The Gas Laws and Absolute Temperature Charles’ Law The volume of a gas is directly proportional to the temperature applied if pressure is kept constant V 1 /T 1 = V 2 /T 2 T must be in Kelvin!

13-7 The Gas Laws and Absolute Temperature Gay-Lussac’s Law The temperature of a gas is directly proportional to the pressure applied if volume is kept constant P 1 /T 1 = P 2 /T 2 T must be in Kelvin!

13-8 The Ideal Gas Law PV  mT One mole (mol) = amount of substance that contains as many atoms or molecules as grams of C-12 SI unit for quantity Atomic mass of H 2 = 2.0 amu (u), molar mass of H 2 = 2.0 g/mol n = mass(g)/molar mass (g/mol), where n = number of moles

13-8 The Ideal Gas Law Ideal Gas Law PV = nRT R = universal gas constant J/mol  K or L  atm/mol  K Ideal gases don’t change phase (?)

13-9 Solving Problems with the Ideal Gas Law STP (standard temperature and pressure) 0  C and 1 atm (101.3 Kpa) Molar volume of a gas (at STP) =22.4L

13-9 Solving Problems with the Ideal Gas Law Combined Gas Law: P 1 V 1 /T 1 = P 2 V 2 /T 2 Its all three gas laws combined

13-10 Ideal Gas Law: Avogadro’s Number Avogadro’s Hypothesis Equal volumes of gases at the same temperature and pressure contain equal number of particles (?)

13-10 Ideal Gas Law: Avogadro’s Number Avogadro’s Number (N A ) Equals the number of particles in a mole »6.02 x 10 23

13-10 Ideal Gas Law: Avogadro’s Number Boltzmann’s Equation Ideal gas law in terms of number of molecules PV = NkT Where K = Boltzmann’ Constant (R/N A ) = 1.38 x J/K N = number of molecules

13-11 Kinetic Theory Kinetic Theory The concept that all matter is made up of atoms which are in constant random motion Based on the assumption that all gases behave like Ideal Gases

13-11 Kinetic Theory Kinetic Theory Ideal Gas (postulates) Particles move in random motion Particles are far part with negligible volume There are no forces between the particles Collisions are perfectly elastic

13-11 Kinetic Theory Kinetic Theory Temperature is related to the average kinetic energy of the particles of a gas KE = ½ mv 2 = 3/2 kT The average translational kinetic energy of molecules in a gas is directly proportional to the absolute temperature Derivation in book (p.400)

13-11 Kinetic Theory Kinetic Theory We can also calculate how fast the particles are moving on the average V rms =  v 2 =  (3kT/m) V rms is the root-mean-square of the velocity of the particles

13-12 Distribution of Molecular Speeds At higher temperatures a larger percent of the molecules are traveling at faster speeds This is why (most) reactions happen quicker at higher temperatures

13-13 Real Gases and Changes of Phase The ideal gas law is an accurate description of the behavior of a real gas as long as the pressure is not too high and the temperature is too low

13-13 Real Gases and Changes of Phase An ideal gas would never change phase because there are no attractive forces between the particles (intermolecular forces). But real gases do.

13-13 Real Gases and Changes of Phase An ideal gas when compressed would just disappear since there is no volume to the individual particles But real gases do not.

13-13 Real Gases and Changes of Phase Adjustments must be made to the universal gas law when dealing with real gases because they are behave differently then ideal gases.

13-13 Real Gases and Changes of Phase At high pressures, the volume of real gases are larger than is predicted by ideal gas behavior. This is due to the actual volume of the gas particles.

13-13 Real Gases and Changes of Phase At low temperatures, the volume of real gases are smaller than is predicted by ideal gas behavior. This is due to the attractive forces of the gas particles.

13-13 Real Gases and Changes of Phase Phase diagram: shows the state of a substance at various temperatures and pressures Phase diagram for water

13-13 Real Gases and Changes of Phase Names of phase changes?

13-13 Real Gases and Changes of Phase What is a triple point? Critical point? Critical temperature?

13-13 Real Gases and Changes of Phase What is the difference between a gas and a vapor?

13-14 Vapor Pressure and Humidity What is the difference between boiling and evaporating?

13-14 Vapor Pressure and Humidity In a closed container of liquid some of the liquid will have evaporated. If equilibrium has been achieved then there is not net change between the amount of vapor and liquid there is in the container.

13-14 Vapor Pressure and Humidity The pressure exerted on the container’s walls by the vapor is called the saturated vapor pressure. This pressure depends on the temperature of the liquid (and gas). What effect on the saturated vapor pressure would raising the temperature have?

13-14 Vapor Pressure and Humidity Relative Humidity: the ratio of the partial pressure of water to the saturated vapor pressure of water at a certain temperature. Partial pressure: the pressure due to one gas in a mixture of gases

13-14 Vapor Pressure and Humidity How can the same amount of water vapor in the air have a different relative humidity depending on the air temperature? Why does 100% humidity feel worse in summer than in winter?

13-14 Vapor Pressure and Humidity Explain the phenomena pictures at the right.

13-14 Vapor Pressure and Humidity What cause dew? What is the dew point? Why does dew point depend on temperature?

13-15 Diffusion Diffusion: the movement of particles from an area of higher concentration to an area of lower concentration. Why does diffusion occur? How does diffusion occur?