Web Resource: Ideal Gas Simulation. Kinetic Theory of Gases. Ideal Gas. Ideal Gas Assumptions
|
|
- Vivian Sharp
- 5 years ago
- Views:
Transcription
1 Web Resource: Ideal Gas Simulation Kinetic Theory of Gases Physics Enhancement Programme Dr. M.H. CHAN, HKBU Link: Ideal Gas Ideal Gas Assumptions The interatomic forces within the gas are ery weak. There is no equilibrium separation for the atoms. Thus, no standard olume at a gien temperature. For a gas, the olume is entirely determined by the container holding the gas. Equations inoling gases will contain the olume, V, as a ariable This is instead of focusing on V The number of molecules in the gas is large, and the aerage separation between the molecules is large compared with their dimensions. The molecules occupy a negligible olume within the container. This is consistent with the macroscopic model where we assumed the molecules were point like. The molecules obey Newton s laws of motion, but as a whole they moe randomly. Any molecule can moe in any direction with any speed. 3 4
2 Ideal Gas Assumptions Notes on Ideal Gas The molecules interact only by short range forces during elastic collisions. This is consistent with the macroscopic model, in which the molecules exert no long range forces on each other. The molecules make elastic collisions with the walls. These collisions lead to the macroscopic pressure on the walls of the container. The gas under consideration is a pure substance. All molecules are identical. An ideal gas is often pictured as consisting of single atoms. Howeer, the behaior of molecular gases approximate that of ideal gases quite well. At low pressures. Molecular rotations and ibrations hae no effect, on aerage, on the motions considered. 5 6 Gas: Equation of State Ideal Gas Model It is useful to know how the olume, pressure and temperature of the gas of mass m are related. The equation that interrelates these quantities is called the equation of state. These are generally quite complicated. If the gas is maintained at a low pressure, the equation of state becomes much easier. This type of a low density gas is commonly referred to as an ideal gas. The ideal gas model can be used to make predictions about the behaior of gases. If the gases are at low pressures, this model adequately describes the behaior of real gases. 7 8
3 The Mole The Mole The amount of gas in a gien olume is coneniently expressed in terms of the number of moles. One mole of any substance is that amount of the substance that contains Aogadro s number of constituent particles. Aogadro s number N A = 6.0 x 0 3. The constituent particles can be atoms or molecules. The number of moles can be determined from the mass of the substance: n = m /M. M is the molar mass of the substance. Example: Helium, M = 4 g/mol. m is the mass of the sample. n is the number of moles. 9 0 Gas Laws Ideal Gas Law Boyle s law: When a gas is kept at a constant temperature, its pressure (P) is inersely proportional to its olume (V). PV = Constant. Charles law: When a gas is kept at a constant pressure, its olume (V) is directly proportional to its temperature (T). V / T = V / T. Guy Lussac s law: When the olume of the gas is kept constant, the pressure (P) is directly proportional to the temperature (T). P / T = P / T. The ideal gas law is the equation of state of a hypothetical ideal gas. The equation of state for an ideal gas combines and summarizes the Ideal Gas Law: PV = nrt R = Uniersal Gas Constant = 8.34 J/mol K = L atm/mol K Example: Determine the olume of any gas ( mole, atmospheric pressure, 0 o C) Answer:.4 L
4 Ideal Gas Law Application: Eco Cooler The ideal gas law is often expressed in terms of the total number of molecules, N, present in the sample. PV = nrt = (N/N A ) RT = Nk B T k B = Boltzmann s constant =.38 x 0 3 J/K It is common to call P, V, and T the thermodynamic ariables of an ideal gas. If the equation of state is known, one of the ariables can always be expressed as some function of the other two. The Eco Cooler is a zero electricity air cooler, which made of plastic bottles. Helps to reduce temperatures in tin huts to make them bearable to lie in. Because of the simplicity, eeryone is expected to be able to adopt this idea and make their own. Reference: green.com/air conditioner less 5/ 3 4 Application: Eco Cooler Application: Eco Cooler The DIY air conditioner has no copyright. Instruction manual is aailable at: cooler/eco Cooler.HowToMake.pdf Blow With you mouth wide open. Blow With you mouth with your lips pursed. Can you relate this effect to thermodynamics? 5 6
5 Molecular Model of an Ideal Gas Pressure and Kinetic Energy Macroscopic properties of a gas were pressure, olume and temperature. Can be related to microscopic description Matter is treated as a collection of molecules. Newton s Laws of Motion can be applied statistically. Assume a container is a cube. Edges are length d. Motion of the molecule: in terms of its elocity components. Momentum and the aerage force. 7 8 Pressure and Kinetic Energy Pressure and Kinetic Energy Assume perfectly elastic collisions with the walls of the container. The relationship between the pressure and the molecular kinetic energy comes from momentum and Newton s Laws. Pressure is proportional to the number of molecules per unit olume (N/V) and to the aerage translational kinetic energy of the molecules: P 3 N V mo This equation relates the macroscopic quantity of pressure with a microscopic quantity of the aerage alue of the square of the molecular speed. Ways to increase pressure: increase the number of molecules per unit olume; and increase the speed (kinetic energy) of the molecules. 9 0
6 Molecular Interpretation of Temperature Total Kinetic Energy Temperature is a direct measure of the aerage molecular kinetic energy: N P mo NkBT 3 V Theorem of Equipartition of Energy: Each translational degree of freedom contributes an equal amount to the energy of the gas mo mo mo mo x y z 3 kbt kbt kbt kbt Total Kinetic Energy (translational): K Tot N m 3 3 NkBT nrt If a gas has only translational energy, this is the internal energy of the gas. Internal energy of an ideal gas depends only on the temperature. RMS Speed Root Mean Square Speed of molecules: 3kT m M = molar mass (in kg per mole) = m o N A RMS o 3RT M Quick Quiz Two containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas, but container B has twice the olume of container A. (i) What is the aerage translational kinetic energy per molecule in container B? [ Answer: (b), translational KE is a function of temperature only ] (ii) Describe the internal energy of the gas in container B. [ Answer: (a), there are twice as many molecules ] Multiple Choices: (a) twice that of container A. (b) the same as that of container A. (c) half that of container A. (d) impossible to determine. 3 4
7 Molar Specific Heat Molar Specific Heat Consider: An ideal gas undergoes seeral processes such that change in temperature is T. Temperature change can be achieed by arious paths (from one isotherm to another). T is the same for each process E int is also the same. Work done on gas (negatie area under the cure) is different for each path. From the first law of thermodynamics (E int = Q + W), the heat associated with a particular change in temperature is not unique. Specific heats for two processes that frequently occur: Changes with constant pressure Changes with constant olume 5 6 Molar Specific Heat Ideal Monatomic Gas Constant olume processes: Q n C Constant pressure processes: Q n C p T T () () Monatomic gas: one atom per molecule. When energy is added to a monatomic gas in a container with a fixed olume, all of the energy goes into increasing the translational kinetic energy of the gas. There is no other way to store energy in such a gas. C = molar specific heat at constant olume C p = molar specific heat at constant pressure Q in Eqn () is greater than Q in Eqn () for a gien n and T. Why? 7 8
8 Exercise on Molar Specific Heat Find: (a) C (molar specific heat at constant olume, State i f ); (b) C p (molar specific heat at constant pressure,, State i f ) of an ideal monatomic gas. Express your answers in terms of R (Uniersal Gas Constant). Answers: C = 3R/ C p = 5R/ Remark: C C p 5 3 Molar Specific Heat of Monatomic Gases Constant Volume: C Constant Pressure: C p Applicable to any ideal gas: 3 R.5 J/ molk 5 R 0.8 J/ molk C p C R 9 30 Molar Specific Heat of Various Gases Quick Quiz ) How does the internal energy (E int ) of an ideal gas change as it follows path i f? ) How does the internal energy of an ideal gas change as it follows path f f along the isotherm labeled T + T? (A) E int increases. (B) E int decreases. (C) E int stays the same. Answers: ) A ) C 3 3
9 Exercise: Heating a cylinder of helium gas Adiabatic Processes A cylinder contains 3 moles helium gas at 300 K. i. The gas is heated at constant olume, calculate the heat required to transfer to the gas in order to increase the temperature to 500 K. ii. The gas is heated at constant pressure, calculate the heat required to transfer to the gas in order to increase the temperature to 500 K. Adiabatic process: No energy is transferred by heat between a system and its surroundings. Assume an ideal gas is in an equilibrium state and PV = nrt is alid. The pressure and olume of an ideal gas at any time during an adiabatic process are related by PV = constant. = C P / C V is assumed to be constant during the process. All three ariables in the ideal gas law (P, V, T ) can change during an adiabatic process Exercise: Adiabatic Process Exercise: Diesel Engine Cylinder Considering an ideal gas undergoes an adiabatic process, proe: i. ii. PV where = C P / C V. i i TV constant T V f f Air (0C) in a diesel engine cylinder is compressed from an initial pressure of atm and a olume of 800 cm 3 to 60 cm 3. Assume air behaes as an ideal gas with =.4 and the compression is adiabatic. Find the final pressure and temperature of the air
10 Equipartition of Energy Equipartition of Energy In addition to internal energy, one possible energy is the translational motion of the center of mass. Rotational motion about the arious axes also contributes. For this molecule, we can neglect the rotation around the y axis since it is negligible compared to the x and z axes. The molecule can also ibrate. There is kinetic energy and potential energy associated with the ibrations Molecular Vibrations Equipartition of Energy Translational motion: 3 degrees of freedom. Rotational motion: degrees of freedom. Vibrational motion: degrees of freedom. Symmetrical Stretching Antisymmetrical Stretching Scissoring Rocking Wagging Twisting Animation Source: Wikipedia Suppose: E C int 3N kbt N kbt N kbt de n dt Translational int 7R Rotational Vibrational 39 40
11 Molar specific heat of hydrogen as a function of temperature. Hydrogen liquefies at 0 K. Complex Molecules For molecules with more than two atoms, the ibrations are more complex. The number of degrees of freedom is larger. The more degrees of freedom aailable to a molecule, the more ibration modes there are to store energy. This results in a higher molar specific heat. 4 4 Quantization of Energy Vibrational states are separated by larger energy gaps than are rotational states. At low temperatures, the energy gained during collisions is generally not enough to raise it to the first excited state of either rotation or ibration. Quantization of Energy As the temperature increases, the speed (or energy) of the molecules increases. In some collisions, the molecules hae enough energy to excite to the first excited state. As the temperature continues to increase, more molecules are in excited states
12 Quantization of Energy ~ Room temperature, rotational energy contributes fully to the internal energy. ~ 000 K, ibrational energy leels are reached. ~0,000 K, ibration contributes fully to the internal energy. Monatomic Gas C = 3R/ C p = 5R/ Diatomic Gas Room Temperature C = 5R/ C p = 7R/ High Temperature C = 7R/ = 5/3 =.67 = 7/5 =.4 Translational only Translational and Rotational Translational, Rotational, and Vibrational Quick Quiz Quick Quiz The molar specific heat of a diatomic gas is measured at constant olume and found to be 9. J/(molK). What are the types of energy that are contributing to the molar specific heat? A. Translation only. B. Translation and rotation only. C. Translation and ibration only. D. Translation, rotation, and ibration. Answer: D [ 9. J/(molK) 7R/ ] The molar specific heat of a gas is measured at constant olume and found to be R/. Is the gas most likely to be A. monatomic, B. diatomic, or C. polyatomic? Answer: C [ C = R/, which is larger than the highest possible alue of C (7R/) for a diatomic gas ] 47 48
13 Web Resource: Kinetic Theory Boltzmann Distribution Law Probability of finding a molecule in a particular energy state: n E n o exp E k T B Web Resource where n V (E ) de is the number of molecules per unit olume with energy between E and E + de Exercise on Number Density Consider a gas at a temperature of 500 K whose atoms can occupy only two energy leels separated by.5 ev. Determine the ratio of the number of atoms in the higher energy leel to the number in the lower energy leel. Ludwig Boltzmann Austrian physicist Contributed to: Kinetic Theory of Gases. Electromagnetism. Thermodynamics. Pioneer in statistical mechanics. 5 5
14 Maxwell Boltzmann Speed Distribution Distribution of speeds in N gas molecules: N P m 4N k o B T M 4 RT 3 3 M = Molar Mass of the Gas [kg], R = Gas Constant = 8.3 J/(molK), T = Temperature [K], and = Speed of Gas Molecules. m o exp kbt M exp RT 0 P d 53 P() (s/m).5 x 0-3 Maxwell's Speed Distribution, M= kg, T= K Speed Distribution Mean Speed RMS Speed Most Probable Speed Escape,Earth =. km/s Speed (km) P() E E E E E-93.04E E Speed (m/s) 54.4 x 0-3 Maxwell's Speed Distribution, M= kg, T= K. Speed Distribution Mean Speed RMS Speed Most Probable Speed Escape,Mercury = 4.5 km/s.6 x 0-3 Maxwell's Speed Distribution, M= kg, T= K.4. Speed Distribution Mean Speed RMS Speed Most Probable Speed Escape,Venus = 0.4 km/s P() (s/m) P( > 4.5 km/s).9e 0 P() (s/m) P( > 0.4 km/s) Speed (m/s) Speed (m/s) 55 56
15 Distribution of Molecular Speeds Distribution of Molecular Speeds Fraction of molecules with speeds in an interal [, ]: Mean Speed: RMS Speed: Fraction[, ] 0 P P( ) d RMS 0 3RT M d 8RT M 3RT P( ) d M 0 57 Most Probable Speed ( mp ): The speed at which P() is maximum. Note: mp dp( ) Sole 0 d RMS RT mp M 58 Maxwell Boltzmann Speed Distribution Speed Distribution As T increases, the peak shifts to the right. This shows that the aerage speed increases with increasing temperature
16 Exercise Summary 0.5 mole hydrogen gas at 300 K. (a) Find the mean speed, the rms speed, and the most probable speed. (b) Find the number of hydrogen molecules with speeds between 400 ms and 40 ms. Answers: (a).78 km/s,.93 km/s,.57 km/s (b).60 9 molecules. 6 6 Summary 63
Chapter 14 Thermal Physics: A Microscopic View
Chapter 14 Thermal Physics: A Microscopic View The main focus of this chapter is the application of some of the basic principles we learned earlier to thermal physics. This will gie us some important insights
More informationSpeed Distribution at CONSTANT Temperature is given by the Maxwell Boltzmann Speed Distribution
Temperature ~ Average KE of each particle Particles have different speeds Gas Particles are in constant RANDOM motion Average KE of each particle is: 3/2 kt Pressure is due to momentum transfer Speed Distribution
More informationRate of Heating and Cooling
Rate of Heating and Cooling 35 T [ o C] Example: Heating and cooling of Water E 30 Cooling S 25 Heating exponential decay 20 0 100 200 300 400 t [sec] Newton s Law of Cooling T S > T E : System S cools
More informationCHAPTER 21 THE KINETIC THEORY OF GASES-PART? Wen-Bin Jian ( 簡紋濱 ) Department of Electrophysics National Chiao Tung University
CHAPTER 1 THE KINETIC THEORY OF GASES-PART? Wen-Bin Jian ( 簡紋濱 ) Department of Electrophysics National Chiao Tung University 1. Molecular Model of an Ideal Gas. Molar Specific Heat of an Ideal Gas. Adiabatic
More informationPhysics 2 week 7. Chapter 3 The Kinetic Theory of Gases
Physics week 7 Chapter 3 The Kinetic Theory of Gases 3.1. Ideal Gases 3.1.1. Experimental Laws and the Equation of State 3.1.. Molecular Model of an Ideal Gas 3.. Mean Free Path 3.3. The Boltzmann Distribution
More informationKinetic Theory. Reading: Chapter 19. Ideal Gases. Ideal gas law:
Reading: Chapter 19 Ideal Gases Ideal gas law: Kinetic Theory p nrt, where p pressure olume n number of moles of gas R 831 J mol -1 K -1 is the gas constant T absolute temperature All gases behae like
More informationChapter 19 Kinetic Theory of Gases
Chapter 9 Kinetic heory of Gases A gas consists of atoms or molecules which collide with the walls of the container and exert a pressure, P. he gas has temperature and occupies a olume V. Kinetic theory
More informationSpeed Distribution at CONSTANT Temperature is given by the Maxwell Boltzmann Speed Distribution
Temperature ~ Average KE of each particle Particles have different speeds Gas Particles are in constant RANDOM motion Average KE of each particle is: 3/2 kt Pressure is due to momentum transfer Speed Distribution
More informationThe Kinetic Theory of Gases
chapter 1 The Kinetic Theory of Gases 1.1 Molecular Model of an Ideal Gas 1. Molar Specific Heat of an Ideal Gas 1.3 Adiabatic Processes for an Ideal Gas 1.4 The Equipartition of Energy 1.5 Distribution
More information(2) The volume of molecules is negligible in comparison to the volume of gas. (3) Molecules of a gas moves randomly in all direction.
9.1 Kinetic Theory of Gases : Assumption (1) The molecules of a gas are identical, spherical and perfectly elastic point masses. (2) The volume of molecules is negligible in comparison to the volume of
More informationChapter 18 Thermal Properties of Matter
Chapter 18 Thermal Properties of Matter In this section we define the thermodynamic state variables and their relationship to each other, called the equation of state. The system of interest (most of the
More informationPhysics 231 Topic 12: Temperature, Thermal Expansion, and Ideal Gases Alex Brown Nov
Physics 231 Topic 12: Temperature, Thermal Expansion, and Ideal Gases Alex Brown Nov 18-23 2015 MSU Physics 231 Fall 2015 1 homework 3 rd midterm final Thursday 8-10 pm makeup Friday final 9-11 am MSU
More informationChapter 13: Temperature, Kinetic Theory and Gas Laws
Chapter 1: Temperature, Kinetic Theory and Gas Laws Zeroth Law of Thermodynamics (law of equilibrium): If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in
More informationChapter 15 Thermal Properties of Matter
Chapter 15 Thermal Properties of Matter To understand the mole and Avogadro's number. To understand equations of state. To study the kinetic theory of ideal gas. To understand heat capacity. To learn and
More informationCh. 19: The Kinetic Theory of Gases
Ch. 19: The Kinetic Theory of Gases In this chapter we consider the physics of gases. If the atoms or molecules that make up a gas collide with the walls of their container, they exert a pressure p on
More informationε tran ε tran = nrt = 2 3 N ε tran = 2 3 nn A ε tran nn A nr ε tran = 2 N A i.e. T = R ε tran = 2
F1 (a) Since the ideal gas equation of state is PV = nrt, we can equate the right-hand sides of both these equations (i.e. with PV = 2 3 N ε tran )and write: nrt = 2 3 N ε tran = 2 3 nn A ε tran i.e. T
More informationLecture 25 Goals: Chapter 18 Understand the molecular basis for pressure and the idealgas
Lecture 5 Goals: Chapter 18 Understand the molecular basis for pressure and the idealgas law. redict the molar specific heats of gases and solids. Understand how heat is transferred via molecular collisions
More informationPart I: Basic Concepts of Thermodynamics
Part I: Basic Concepts of Thermodynamics Lecture 3: Heat and Work Kinetic Theory of Gases Ideal Gases 3-1 HEAT AND WORK Here we look in some detail at how heat and work are exchanged between a system and
More informationPhysics 207 Lecture 25. Lecture 25, Nov. 26 Goals: Chapter 18 Understand the molecular basis for pressure and the idealgas
Lecture 25, Nov. 26 Goals: Chapter 18 Understand the molecular basis for pressure and the idealgas law. redict the molar specific heats of gases and solids. Understand how heat is transferred via molecular
More informationHandout 11: Ideal gas, internal energy, work and heat. Ideal gas law
Handout : Ideal gas, internal energy, work and heat Ideal gas law For a gas at pressure p, volume V and absolute temperature T, ideal gas law states that pv = nrt, where n is the number of moles and R
More informationDownloaded from
Chapter 13 (Kinetic Theory) Q1. A cubic vessel (with face horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of500 ms in vertical direction.
More informationHandout 11: Ideal gas, internal energy, work and heat. Ideal gas law
Handout : Ideal gas, internal energy, work and heat Ideal gas law For a gas at pressure p, volume V and absolute temperature T, ideal gas law states that pv = nrt, where n is the number of moles and R
More informationChapter 19: The Kinetic Theory of Gases Questions and Example Problems
Chapter 9: The Kinetic Theory of Gases Questions and Example Problems N M V f N M Vo sam n pv nrt Nk T W nrt ln B A molar nmv RT k T rms B p v K k T λ rms avg B V M m πd N/V Q nc T Q nc T C C + R E nc
More informationKINETICE THEROY OF GASES
INTRODUCTION: Kinetic theory of gases relates the macroscopic properties of gases (like pressure, temperature, volume... etc) to the microscopic properties of the gas molecules (like speed, momentum, kinetic
More informationChapter 17 Temperature & Kinetic Theory of Gases 1. Thermal Equilibrium and Temperature
Chapter 17 Temperature & Kinetic Theory of Gases 1. Thermal Equilibrium and Temperature Any physical property that changes with temperature is called a thermometric property and can be used to measure
More informationThermodynamics Molecular Model of a Gas Molar Heat Capacities
Thermodynamics Molecular Model of a Gas Molar Heat Capacities Lana Sheridan De Anza College May 3, 2018 Last time modeling an ideal gas at the microscopic level rms speed of molecules equipartition of
More informationThermodynamics: Microscopic vs. Macroscopic (Chapters 16, )
Thermodynamics: Microscopic vs. Macroscopic (Chapters 16, 18.1-5 ) Matter and Thermal Physics Thermodynamic quantities: Volume V and amount of substance Pressure P Temperature T: Ideal gas Zeroth Law of
More informationChapter 16. Kinetic Theory of Gases. Summary. molecular interpretation of the pressure and pv = nrt
Chapter 16. Kinetic Theory of Gases Summary molecular interpretation of the pressure and pv = nrt the importance of molecular motions elocities and speeds of gas molecules distribution functions for molecular
More informationChapter 10. Thermal Physics. Thermodynamic Quantities: Volume V and Mass Density ρ Pressure P Temperature T: Zeroth Law of Thermodynamics
Chapter 10 Thermal Physics Thermodynamic Quantities: Volume V and Mass Density ρ Pressure P Temperature T: Zeroth Law of Thermodynamics Temperature Scales Thermal Expansion of Solids and Liquids Ideal
More informationThermal Properties of Matter (Microscopic models)
Chapter 18 Thermal Properties of Matter (Microscopic models) PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 6_18_2012
More informationQuickCheck. Collisions between molecules. Collisions between molecules
Collisions between molecules We model molecules as rigid spheres of radius r as shown at the right. The mean free path of a molecule is the average distance it travels between collisions. The average time
More informationPhysics 4C Chapter 19: The Kinetic Theory of Gases
Physics 4C Chapter 19: The Kinetic Theory of Gases Whether you think you can or think you can t, you re usually right. Henry Ford The only thing in life that is achieved without effort is failure. Source
More informationLecture 3. The Kinetic Molecular Theory of Gases
Lecture 3. The Kinetic Molecular Theory of Gases THE IDEAL GAS LAW: A purely empirical law solely the consequence of experimental observations Explains the behavior of gases over a limited range of conditions
More informationChapter 10. Thermal Physics
Chapter 10 Thermal Physics Thermal Physics Thermal physics is the study of Temperature Heat How these affect matter Thermal Physics, cont Descriptions require definitions of temperature, heat and internal
More informationCollisions between molecules
Collisions between molecules We model molecules as rigid spheres of radius r as shown at the right. The mean free path of a molecule is the average distance it travels between collisions. The average time
More informationUnit 05 Kinetic Theory of Gases
Unit 05 Kinetic Theory of Gases Unit Concepts: A) A bit more about temperature B) Ideal Gas Law C) Molar specific heats D) Using them all Unit 05 Kinetic Theory, Slide 1 Temperature and Velocity Recall:
More informationThe Kinetic Theory of Gases
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
More informationChemical Thermodynamics : Georg Duesberg
The Properties of Gases Kinetic gas theory Maxwell Boltzman distribution, Collisions Real (non-ideal) gases fugacity, Joule Thomson effect Mixtures of gases Entropy, Chemical Potential Liquid Solutions
More informationPV = n R T = N k T. Measured from Vacuum = 0 Gauge Pressure = Vacuum - Atmospheric Atmospheric = 14.7 lbs/sq in = 10 5 N/m
PV = n R T = N k T P is the Absolute pressure Measured from Vacuum = 0 Gauge Pressure = Vacuum - Atmospheric Atmospheric = 14.7 lbs/sq in = 10 5 N/m V is the volume of the system in m 3 often the system
More informationThe Kinetic Theory of Gases
978-1-107-1788-3 Classical and Quantum Thermal Physics The Kinetic Theory of Gases CHAPTER 1 1.0 Kinetic Theory, Classical and Quantum Thermodynamics Two important components of the unierse are: the matter
More informationPhysics 231 Lecture 30. Main points of today s lecture: Ideal gas law:
Physics 231 Lecture 30 Main points of today s lecture: Ideal gas law: PV = nrt = Nk BT 2 N 1 2 N 3 3 V 2 3 V 2 2 P = m v = KE ; KE KE = kbt Phases of Matter Slide 12-16 Ideal Gas: properties Approximate
More informationKINETIC THEORY OF GASES
KINETIC THEORY OF GASES VERY SHORT ANSWER TYPE QUESTIONS ( MARK). Write two condition when real gases obey the ideal gas equation ( nrt). n number of mole.. If the number of molecule in a container is
More informationMP203 Statistical and Thermal Physics. Jon-Ivar Skullerud and James Smith
MP203 Statistical and Thermal Physics Jon-Ivar Skullerud and James Smith October 3, 2017 1 Contents 1 Introduction 3 1.1 Temperature and thermal equilibrium.................... 4 1.1.1 The zeroth law of
More informationLecture 24. Ideal Gas Law and Kinetic Theory
Lecture 4 Ideal Gas Law and Kinetic Theory Today s Topics: Ideal Gas Law Kinetic Theory of Gases Phase equilibria and phase diagrams Ideal Gas Law An ideal gas is an idealized model for real gases that
More informationKINETIC THEORY OF GASES
KINETIC THEORY OF GASES Boyle s Law: At constant temperature volume of given mass of gas is inversely proportional to its pressure. Charle s Law: At constant pressure volume of a given mass of gas is directly
More informationTurning up the heat: thermal expansion
Lecture 3 Turning up the heat: Kinetic molecular theory & thermal expansion Gas in an oven: at the hot of materials science Here, the size of helium atoms relative to their spacing is shown to scale under
More information12.1 Work in Thermodynamic Processes
Name APPH7_Notes3key Page 1 of 6 AP Physics Date Notes: Thermodynamics 12.1 Work in Thermodynamic Processes First Law of Thermodynamics The First Law of Thermodynamics tells us that the internal energy
More informationIdeal Gas Behavior. NC State University
Chemistry 331 Lecture 6 Ideal Gas Behavior NC State University Macroscopic variables P, T Pressure is a force per unit area (P= F/A) The force arises from the change in momentum as particles hit an object
More informationChapter 10: Thermal Physics
Chapter 10: hermal Physics hermal physics is the study of emperature, Heat, and how these affect matter. hermal equilibrium eists when two objects in thermal contact with each other cease to echange energy.
More informationKinetic Theory of Gases
Kinetic Theory of Gases Modern Physics September 7 and 12, 2016 1 Intro In this section, we will relate macroscopic properties of gases (like Pressure, Temperature) to the behavior of the microscopic components
More informationThis is a statistical treatment of the large ensemble of molecules that make up a gas. We had expressed the ideal gas law as: pv = nrt (1)
1. Kinetic Theory of Gases This is a statistical treatment of the large ensemble of molecules that make up a gas. We had expressed the ideal gas law as: pv = nrt (1) where n is the number of moles. We
More informationPhase Changes and Latent Heat
Review Questions Why can a person remove a piece of dry aluminum foil from a hot oven with bare fingers without getting burned, yet will be burned doing so if the foil is wet. Equal quantities of alcohol
More informationPHYSICS - CLUTCH CH 19: KINETIC THEORY OF IDEAL GASSES.
!! www.clutchprep.com CONCEPT: ATOMIC VIEW OF AN IDEAL GAS Remember! A gas is a type of fluid whose volume can change to fill a container - What makes a gas ideal? An IDEAL GAS is a gas whose particles
More informationMolecular Motion and Gas Laws
Molecular Motion and Gas Laws What is the connection between the motion of molecules (F = ma and K = mv 2 /2) and the thermodynamics of gases (pv = nrt and U = 3nRT/2)? In this lab, you will discover how
More information10 TEMPERATURE, THERMAL EXPANSION, IDEAL GAS LAW, AND KINETIC THEORY OF GASES.
10 TEMPERATURE, THERMAL EXPANSION, IDEAL GAS LAW, AND KINETIC THEORY OF GASES. Key words: Atoms, Molecules, Atomic Theory of Matter, Molecular Mass, Solids, Liquids, and Gases, Thermodynamics, State Variables,
More informationKINETIC THEORY. was the original mean square velocity of the gas. (d) will be different on the top wall and bottom wall of the vessel.
Chapter Thirteen KINETIC THEORY MCQ I 13.1 A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of 500m s 1
More informationAtomic Mass and Atomic Mass Number. Moles and Molar Mass. Moles and Molar Mass
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
More informationNY Times 11/25/03 Physics L 22 Frank Sciulli slide 1
NY Times /5/03 slide Thermodynamics and Gases Last Time specific heats phase transitions Heat and Work st law of thermodynamics heat transfer conduction convection radiation Today Kinetic Theory of Gases
More informationChapter 14 Thermal Physics: A Microscopic View
Chapter 14 Thermal Physics: Microscopic View The main focus of this chapter is the application of some of the basic principles we learned earlier to thermal physics. This will give us some important insights
More informationIdeal Gases. 247 minutes. 205 marks. theonlinephysicstutor.com. facebook.com/theonlinephysicstutor. Name: Class: Date: Time: Marks: Comments:
Ideal Gases Name: Class: Date: Time: 247 minutes Marks: 205 marks Comments: Page 1 of 48 1 Which one of the graphs below shows the relationship between the internal energy of an ideal gas (y-axis) and
More informationKinetic theory of the ideal gas
Appendix H Kinetic theory of the ideal gas This Appendix contains sketchy notes, summarizing the main results of elementary kinetic theory. The students who are not familiar with these topics should refer
More informationMolar Specific Heat of Ideal Gases
Molar Specific Heat of Ideal Gases Since Q depends on process, C dq/dt also depends on process. Define a) molar specific heat at constant volume: C V (1/n) dq/dt for constant V process. b) molar specific
More informationHomework: 13, 14, 18, 20, 24 (p )
Homework: 13, 14, 18, 0, 4 (p. 531-53) 13. A sample of an ideal gas is taken through the cyclic process abca shown in the figure below; at point a, T=00 K. (a) How many moles of gas are in the sample?
More informationThermodynamics. Atoms are in constant motion, which increases with temperature.
Thermodynamics SOME DEFINITIONS: THERMO related to heat DYNAMICS the study of motion SYSTEM an object or set of objects ENVIRONMENT the rest of the universe MICROSCOPIC at an atomic or molecular level
More information11/22/2010. Mid term results. Thermal physics
Mid term results Thermal physics 1 Zeroth law of thermodynamics If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other.
More informationPhysics 160 Thermodynamics and Statistical Physics: Lecture 2. Dr. Rengachary Parthasarathy Jan 28, 2013
Physics 160 Thermodynamics and Statistical Physics: Lecture 2 Dr. Rengachary Parthasarathy Jan 28, 2013 Chapter 1: Energy in Thermal Physics Due Date Section 1.1 1.1 2/3 Section 1.2: 1.12, 1.14, 1.16,
More informationChapter 17. Temperature. Dr. Armen Kocharian
Chapter 17 Temperature Dr. Armen Kocharian Temperature We associate the concept of temperature with how hot or cold an objects feels Our senses provide us with a qualitative indication of temperature Our
More information17-1 Ideal Gases. Gases are the easiest state of matter to describe - All ideal gases exhibit similar behavior.
17-1 Ideal Gases Gases are the easiest state of matter to describe - All ideal gases exhibit similar behavior. An ideal gas is one that is thin enough, that the interactions between molecules can be ignored.
More information18.13 Review & Summary
5/2/10 10:04 PM Print this page 18.13 Review & Summary Temperature; Thermometers Temperature is an SI base quantity related to our sense of hot and cold. It is measured with a thermometer, which contains
More informationGASES (Chapter 5) Temperature and Pressure, that is, 273 K and 1.00 atm or 760 Torr ) will occupy
I. Ideal gases. A. Ideal gas law review. GASES (Chapter 5) 1. PV = nrt Ideal gases obey this equation under all conditions. It is a combination ofa. Boyle's Law: P 1/V at constant n and T b. Charles's
More informationThermal Physics. 1) Thermodynamics: Relates heat + work with empirical (observed, not derived) properties of materials (e.g. ideal gas: PV = nrt).
Thermal Physics 1) Thermodynamics: Relates heat + work with empirical (observed, not derived) properties of materials (e.g. ideal gas: PV = nrt). 2) Statistical Mechanics: Uses models (can be more complicated)
More informationExample Problems: 1.) What is the partial pressure of: Total moles = 13.2 moles 5.0 mol A 7.0 mol B 1.2 mol C Total Pressure = 3.
5.6 Dalton s Law of Partial Pressures Dalton s Law of Partial Pressure; The total pressure of a gas is the sum of all its parts. P total = P 1 + P + P 3 + P n Pressures are directly related to moles: n
More informationLecture 24. Ideal Gas Law and Kinetic Theory
Lecture 4 Ideal Gas Law and Kinetic Theory Today s Topics: Ideal Gas Law Kinetic Theory of Gases Phase equilibria and phase diagrams Ideal Gas Law An ideal gas is an idealized model for real gases that
More informationWeek 1 Temperature, Heat and the First Law of Thermodynamics. (Ch. 19 of Serway&J.)
Week 1 Temperature, Heat and the First Law of Thermodynamics. (Ch. 19 of Serway&J.) (Syllabus) Temperature Thermal Expansion Temperature and Heat Heat and Work The first Law Heat Transfer Temperature Thermodynamics:
More informationSpecific Heat of Diatomic Gases and. The Adiabatic Process
Specific Heat of Diatomic Gases and Solids The Adiabatic Process Ron Reifenberger Birck Nanotechnology Center Purdue University February 22, 2012 Lecture 7 1 Specific Heat for Solids and Diatomic i Gasses
More informationGases and Kinetic Theory
Gases and Kinetic Theory Chemistry 35 Fall 2000 Gases One of the four states of matter Simplest to understand both physically and chemically Gas Properties Low density Fluid Can be defined by their: 1.
More informationModule 5: Rise and Fall of the Clockwork Universe. You should be able to demonstrate and show your understanding of:
OCR B Physics H557 Module 5: Rise and Fall of the Clockwork Universe You should be able to demonstrate and show your understanding of: 5.2: Matter Particle model: A gas consists of many very small, rapidly
More informationThe first law of thermodynamics continued
Lecture 7 The first law of thermodynamics continued Pre-reading: 19.5 Where we are The pressure p, volume V, and temperature T are related by an equation of state. For an ideal gas, pv = nrt = NkT For
More informationKinetic theory. Collective behaviour of large systems Statistical basis for the ideal gas equation Deviations from ideality
Kinetic theory Collective behaviour of large systems Statistical basis for the ideal gas equation Deviations from ideality Learning objectives Describe physical basis for the kinetic theory of gases Describe
More information(Heat capacity c is also called specific heat) this means that the heat capacity number c for water is 1 calorie/gram-k.
Lecture 23: Ideal Gas Law and The First Law of Thermodynamics 1 (REVIEW) Chapter 17: Heat Transfer Origin of the calorie unit A few hundred years ago when people were investigating heat and temperature
More informationPhysics 1501 Lecture 35
Physics 1501: Lecture 35 Todays Agenda Announcements Homework #11 (Dec. 2) and #12 (Dec. 9): 2 lowest dropped Honors students: see me after the class! Todays topics Chap.16: Temperature and Heat» Latent
More informationLesson 12. Luis Anchordoqui. Physics 168. Tuesday, November 28, 17
Lesson 12 Physics 168 1 Temperature and Kinetic Theory of Gases 2 Atomic Theory of Matter On microscopic scale, arrangements of molecules in solids, liquids, and gases are quite different 3 Temperature
More informationPhysics 161 Lecture 14 Kinetic Theory of Gas. October 18, 2018
Physics 161 Lecture 14 Kinetic Theory of Gas October 18, 2018 1 Exam 1, Thursday 18 Oct The exam will start promptly at 10:00pm. You will be permitted to open your exam at 10:00pm. You will have until
More informationCHAPTER III: Kinetic Theory of Gases [5%]
CHAPTER III: Kinetic Theory of Gases [5%] Introduction The kinetic theory of gases (also known as kinetic-molecular theory) is a law that explains the behavior of a hypothetical ideal gas. According to
More informationLecture Outline Chapter 17. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.
Lecture Outline Chapter 17 Physics, 4 th Edition James S. Walker Chapter 17 Phases and Phase Changes Ideal Gases Kinetic Theory Units of Chapter 17 Solids and Elastic Deformation Phase Equilibrium and
More informationIntroduction to Thermodynamic Cycles Part 1 1 st Law of Thermodynamics and Gas Power Cycles
Introduction to Thermodynamic Cycles Part 1 1 st Law of Thermodynamics and Gas Power Cycles by James Doane, PhD, PE Contents 1.0 Course Oeriew... 4.0 Basic Concepts of Thermodynamics... 4.1 Temperature
More informationChapter 14 Kinetic Theory
Chapter 14 Kinetic Theory Kinetic Theory of Gases A remarkable triumph of molecular theory was showing that the macroscopic properties of an ideal gas are related to the molecular properties. This is the
More informationA thermodynamic system is taken from an initial state X along the path XYZX as shown in the PV-diagram.
AP Physics Multiple Choice Practice Thermodynamics 1. The maximum efficiency of a heat engine that operates between temperatures of 1500 K in the firing chamber and 600 K in the exhaust chamber is most
More informationAnnouncements 13 Nov 2014
Announcements 13 Nov 2014 1. Prayer 2. Exam 3 starts on Tues Nov 25 a. Covers Ch 9-12, HW 18-24 b. Late fee on Wed after Thanksgiving, 3 pm c. Closes on Thursday after Thanksgiving, 3 pm d. Jerika review
More informationIf the dividing wall were allowed to move, which of the following statements would not be true about its equilibrium position?
PHYS 213 Exams Database Midterm (A) A block slides across a rough surface, eventually coming to a stop. 1) What happens to the block's internal thermal energy and entropy? a. and both stay the same b.
More informationProcess Nature of Process
AP Physics Free Response Practice Thermodynamics 1983B. The pv-diagram above represents the states of an ideal gas during one cycle of operation of a reversible heat engine. The cycle consists of the following
More informationUNIVERSITY OF SOUTHAMPTON
UNIVERSITY OF SOUTHAMPTON PHYS1013W1 SEMESTER 2 EXAMINATION 2014-2015 ENERGY AND MATTER Duration: 120 MINS (2 hours) This paper contains 8 questions. Answers to Section A and Section B must be in separate
More informationChapter 19 Entropy Pearson Education, Inc. Slide 20-1
Chapter 19 Entropy Slide 20-1 Ch 19 & 20 material What to focus on? Just put out some practice problems Ideal gas how to find P/V/T changes. E.g., gas scaling, intro to the ideal gas law, pressure cooker,
More informationPHYSICS 220. Lecture 22. Textbook Sections Lecture 22 Purdue University, Physics 220 1
PHYSICS 220 Lecture 22 Temperature and Ideal Gas Textbook Sections 14.1 14.3 Lecture 22 Purdue University, Physics 220 1 Overview Last Lecture Speed of sound v = sqrt(b/ρ) Intensity level β = (10 db) log
More informationChapter 11 Gases 1 Copyright McGraw-Hill 2009
Chapter 11 Gases Copyright McGraw-Hill 2009 1 11.1 Properties of Gases The properties of a gas are almost independent of its identity. (Gas molecules behave as if no other molecules are present.) Compressible
More informationADIABATIC PROCESS Q = 0
THE KINETIC THEORY OF GASES Mono-atomic Fig.1 1 3 Average kinetic energy of a single particle Fig.2 INTERNAL ENERGY U and EQUATION OF STATE For a mono-atomic gas, we will assume that the total energy
More informationChapter 19 Entropy Pearson Education, Inc. Slide 20-1
Chapter 19 Entropy Slide 20-1 Ch 19 & 20 material What to focus on? Just put out some practice problems for Ch. 19/20 Ideal gas how to find P/V/T changes. How to calculate energy required for a given T
More informationAlthough different gasses may differ widely in their chemical properties, they share many physical properties
IV. Gases (text Chapter 9) A. Overview of Chapter 9 B. Properties of gases 1. Ideal gas law 2. Dalton s law of partial pressures, etc. C. Kinetic Theory 1. Particulate model of gases. 2. Temperature and
More informationChem 4521 Kinetic Theory of Gases PhET Simulation
Chem 451 Kinetic Theory of Gases PhET Simulation http://phet.colorado.edu/get_phet/simlauncher.php The discussion in the first lectures centered on the ideal gas equation of state and the modifications
More informationChapter 10 Notes: Gases
Chapter 10 Notes: Gases Watch Bozeman Videos & other videos on my website for additional help: Big Idea 2: Gases 10.1 Characteristics of Gases Read p. 398-401. Answer the Study Guide questions 1. Earth
More information