# 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)

Save this PDF as:

Size: px
Start display at page:

Download "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)"

## Transcription

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 can also express it as: pv = NkT () where N is the number of molecules and k is Boltzmann s constant k = R/N A J/K. A volume of air the size of a birthday balloon contains some 10 3 molecules. The very large number of molecules allows us to treat gases using statistics, in which averages of quantities such as speed appear rather than their values for individual molecules.. Pressure and Molecular Motion Consider a container of dilute gas that consists of N independent molecules each of mass m. Pressure is due to molecular collisions with the walls of the container. We need to calculate the average rate of momentum transfer. Suppose we have a container in thermal equilibrium at temperature T with volume V. The molecules are moving in random directions and the average velocity of the molecules is zero (as many are moving in one direction as the other). v = 0 v x = v y = v z (3) While the average velocity is zero, the average speed is not zero. We will concentrate on v which is the root mean square (rms) speed. so The internal energy U consists mainly of the kinetic energies of the molecules U = N K = N ( ) 1 m v (4) 1

2 where K is the average kinetic energy per molecule and N is the total number of molecules. The average of a sum of terms is the sum of the averages of those terms so v = v x + v y + v z = v x + v y + v z (5) v x = v y = v z (6) So we can relate the average of the components of the velocity squared to the thermal energy of the gas: v = 3 v x (7) vx = 1 3 v = U 3 mn (8) a. The Origin of Pressure Pressure arises from the multiple collisions the molecules of a gas have with the walls that contain the gas. First we compute the momentum transfer to a wall due to a single collision, and then find the number of molecules that strike the wall per unit time. A molecule colliding elastically with the right-hand wall of a box, only the x-component of velocity changes so the velocity before collision is: the velocity after collision is: The momentum change of the molecule P mol is v i = v x î + v y ĵ + v zˆk (9) v f = v x î + v y ĵ + v zˆk (10) P mol = m v f m v i = mv x î (11) and the momentum transfer to the wall is P = mv x î (1) The number of collisions with the wall that occur per unit time is calculated as follows. Consider the number of molecules that with an x-component velocity v x

3 that strike an area A in a time interval dt is the number of molecules contained in an imaginary cylinder whose base is against the wall of area A and length v x dt. If the number of molecules per unit volume is N/V, the total number of molecules in the cylinder is (N/V (v x dt)a and the number of collisions in time dt will be half this number as 1/ of the molecules are moving to the right and 1/ to the left. N coll = 1 N V (v xdt)a (13) We can multiply this by the individual collision momentum transfer to find the momentum dp x transferred in time dt. ( ) 1 N dp x = (mv x ) V (v xdt)a = mvx N Adt (14) V The force exerted on the area A is dp x dt = F x = mvx N V A (15) and the pressure on the wall p is the force per unit area p = F x A = N mv x (16) V Finally, recall that we have employed the average x-component of velocity squared for each molecule. We make this explicit by employing the notation vx and find p = m vx N ( ) U N V = m 3mN V = 3 U V (17) pv = 3 U (18) This is an important derivation, as we have used the microscopic properties of a gas to find a relation between macroscopic thermodynamic variables. b. The Meaning of Temperature The fact that the energy is the sum of the kinetic energy of all the molecules U = 1 M, v, and the fact that energy is related to pressure U = (3/)pV provides a link to temperature. 3

4 U = 3 nrt = 3 NkT (19) to give the microscopic interpretation of temperature: kt = U 3 N = K (0) 3 The temperature of an ideal gas is a measure of the average kinetic energy of the constituents. Because the number of molecules canceled, T is independent of the amount of gas. note: absolute zero in the Kelvin scale is the point at which the pressure drops to zero. In the microscopic view of an ideal gas, the temperature is zero when the average kinetic energy of the ideal gas is zero. Pressure vanished because the molecules no longer mover around and bounce against the walls. c. Specific Heat of the Perfect Gas We will consider the energy and specific heat at vanishing density (perfect gases). The energy of the molecules of a gas can be divided into: 1. Translatory kinetic energy. Rotational kinetic energy 3. Energy of vibration of atoms relative to center of mass of whole molecule 4. Mutual potential energy (not relevant for ideal gasses) i. Equipartition The total average energy per molecule depends on how many independent motions a molecule can have. Point mass Energy has three terms propotional to v x,v y and v z Diatomic With rotational inertia about axes x and y we have two new terms in the energy (making it five). Vibration Brings two more terms related to the relative speed of the atomic constituents and separation (making it seven). 4

5 Every term in the energy expression that is quadrati in an independent dynamical variable designates a degree of freedom. The contribution of each degree of freedom to the average energy of a molecule is kt/. This is the equipartition theorem. E = s kt (1) and E can contain contributions associated with translation, rotation and vibration. Translatory Energy U = U t and in specific quantities u = u t = 3 kt = 3 RT. This is exactly the same as the example we had done above. Helium, Neon Argon, Krypton, Xenon. u = 3 RT () c v = 3 R (3) c p = R + c v = 5 R (4) γ = c p /c v = 5/3 (5) Rotational Energy For two atoms rigidly united we have two more degrees of freedom u = u t + u r = 5 kt = 5 RT H, HCl, N, CO, O, NO u = 5 RT (6) c v = 5 R (7) c p = R + c v = 7 R (8) γ = c p /c v = 7/5 (9) For three atoms rigidly united we have three more degrees of freedom u = 5

6 u t + u r = 3kT = 3RT However, classical theory breaks down for this. u = 3RT (30) c v = 3R (31) c p = R + c v = 4R (3) γ = c p /c v = 4/3 (33) Vibration For the temperatures of our atmosphere, we will not deal with this. d. Velocity Distribution of Gases We define the velocity distribution function F ( v) as the probability distribution for the velocities of the gas molecules. The probability of finding any particular velocity v is zero, so we start with a number distribution N( v) such that N( v)d 3 v= number of molecules between v and v + d v and d 3 v = dv x dv y dv z. The total number of molecules is N so that N( v)d 3 v = N (34) The probability distribution F ( v) = 1 N( v), is defined such that F N ( v)d3 v= is the probability that a gas molecule velocity is between v and v + d v. From here we can calculate the average velocity squared: v = v F ( v)d 3 v (35) To determine F ( v) we make the assumption that any way in which a gas s total energy and total momentum (which is zero) can be shared among the molecules is equally likely. When this is assumed, the distribution function is found to be: F ( v) = ( m ) 3/ e mv /kt πkt (36) 6

7 3. Collisions and Transport Phenomena Molecules follow a tortuous path in their container, colliding with one another and the walls. At STP an air molecule undergoes billions of collisions per second, but the average distance a molecule travels between collisions is a statistical quantity that can be calculated. By these collisions, molecules can carry thermal energy, odor, etc. The movement of molecules by random collisions is called diffusion. Molecules of diameter D collide when the path of the center of one molecule lies within an area πd presented by the second molecule. The area is the collision cross section σ. σ = πd. A molecule that moves with speed v and sweeps out an area σ sweeps out a volume V = σd = σvt in a time t. However, the molecule is not alone and encounters N collisions, but even if the path is bent, the volume V remains unchanged. There are on average a collision every τ = t/n seconds. τ is the mean collision time. Averaging over many molecules we replace v with v rms. τ = t N = t nv = t nσv rms t = 1 (37) nσv rms where n = N/V is the number density (not the number of moles). A more precise calculation takes into account the fact that the other molecules are also moving τ = 1 nσvrms (38) The average distance that a molecule travels before it is involved in a collision is the mean free path λ where λ = τv rms = 1 nσ (39) λ is inversely proportional to both the density and the collision cross section. 3a. Random Walk and Diffusion Molecules move through a gas by diffusion. The average distance moved by a molecule is similar to the random walk problem (or drunkard s walk). In this problem, a drunkard starts at a lamppost and takes steps that are equal in length but random in direction. We can find the average displacement of the molecule after 7

8 N steps as follows. Let the successive displacements be L 1, L... L n all of random directions but magnitude L. After N steps the displacement of the molecule is R N = L 1 + L L n. Squaring this quantity we have: R N = L 1 + L L N + L 1 L + L 1 L L N 1 L N (40) In the averaging process, all the dot products have an average value over time of zero, whereas the squared terms are equal to L. R N = NL (41) Connecting this with the properties of a gas. L = λ, after N steps the time is t = τn r = t τ λ (4) It is typical in random walk problems that the displacement squared is linear in time or that the displacement is proportional to the square root of the time. 8

### Ch. 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

### Chapter 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

### MP203 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

### Lecture 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

### Physics 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,

### KINETIC 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

### Rate 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

### Kinetic Model of Gases

Kinetic Model of Gases Section 1.3 of Atkins, 6th Ed, 24.1 of Atkins, 7th Ed. 21.1 of Atkins, 8th Ed., and 20.1 of Atkins, 9th Ed. Basic Assumptions Molecular Speeds RMS Speed Maxwell Distribution of Speeds

### Physics 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

### If the position of a molecule is measured after increments of 10, 100, 1000 steps, what will the distribution of measured steps look like?

If the position of a molecule is measured after increments of 10, 100, 1000 steps, what will the distribution of measured steps look like? (1) No longer Gaussian (2) Identical Gaussians (3) Gaussians with

### 19-9 Adiabatic Expansion of an Ideal Gas

19-9 Adiabatic Expansion of an Ideal Gas Learning Objectives 19.44 On a p-v diagram, sketch an adiabatic expansion (or contraction) and identify that there is no heat exchange Q with the environment. 19.45

### Kinetic 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

### The 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

### Speed 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

### Lecture 18 Molecular Motion and Kinetic Energy

Physical Principles in Biology Biology 3550 Fall 2017 Lecture 18 Molecular Motion and Kinetic Energy Monday, 2 October c David P. Goldenberg University of Utah goldenberg@biology.utah.edu Fick s First

### Why study gases? A Gas 10/17/2017. An understanding of real world phenomena. An understanding of how science works.

Kinetic Theory and the Behavior of Ideal & Real Gases Why study gases? n understanding of real world phenomena. n understanding of how science works. Gas Uniformly fills any container. Mixes completely

### Perfect Gases Transport Phenomena

Perfect Gases Transport Phenomena We have been able to relate quite a few macroscopic properties of gasses such as P, V, T to molecular behaviour on microscale. We saw how macroscopic pressure is related

### Gases 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.

### Unit 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:

### Gas Density. Standard T & P (STP) 10/29/2011. At STP, 1 mol of any ideal gas occupies 22.4 L. T = 273 K (0 o C) P = 1 atm = kpa = 1.

Standard T & P (STP) T = 73 K (0 o C) P = 1 atm = 101.35 kpa = 1.0135 bar At STP, 1 mol of any ideal gas occupies.4 L.4 L Gas Density We can use PV = nrt to determine the density of gases. What are the

### Specific 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

### Lecture 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

### 17-6 The Gas Laws and Absolute Temperature

17-6 The Gas Laws and Absolute Temperature The relationship between the volume, pressure, temperature, and mass of a gas is called an equation of state. We will deal here with gases that are not too dense.

### Chapter 3 - First Law of Thermodynamics

Chapter 3 - dynamics The ideal gas law is a combination of three intuitive relationships between pressure, volume, temp and moles. David J. Starling Penn State Hazleton Fall 2013 When a gas expands, it

### Kinetic Theory of Gases

Kinetic Theory of Gases Chapter 3 P. J. Grandinetti Chem. 4300 Aug. 28, 2017 P. J. Grandinetti (Chem. 4300) Kinetic Theory of Gases Aug. 28, 2017 1 / 45 History of ideal gas law 1662: Robert Boyle discovered

### 18.13 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

### The Kinetic-Molecular Theory of Gases

The Kinetic-Molecular Theory of Gases kinetic-molecular theory of gases Originated with Ludwig Boltzman and James Clerk Maxwell in the 19th century Explains gas behavior on the basis of the motion of individual

### Gases. Measuring Temperature Fahrenheit ( o F): Exceptions to the Ideal Gas Law. Kinetic Molecular Theory

Ideal gas: a gas in which all collisions between atoms or molecules are perfectly elastic (no energy lost) there are no intermolecular attractive forces Think of an ideal gas as a collection of perfectly

### 3. Basic Concepts of Thermodynamics Part 2

3. Basic Concepts of Thermodynamics Part 2 Temperature and Heat If you take a can of cola from the refrigerator and leave it on the kitchen table, its temperature will rise-rapidly at first but then more

### Thermodynamics Lecture Series

Thermodynamics ecture Series Reference: Chap 0 Halliday & Resnick Fundamental of Physics 6 th edition Kinetic Theory of Gases Microscopic Thermodynamics Applied Sciences Education Research Group (ASERG)

### The Kinetic-Molecular Theory of Gases

The Kinetic-Molecular Theory of Gases kinetic-molecular theory of gases Originated with Ludwig Boltzman and James Clerk Maxwell in the 19th century Explains gas behavior on the basis of the motion of individual

### 10 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,

### Chapter 5. The Gas Laws

Chapter 5 The Gas Laws 1 Pressure Force per unit area. Gas molecules fill container. Molecules move around and hit sides. Collisions are the force. Container has the area. Measured with a barometer. 2

### Physics 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

### UNIVERSITY 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

### C p = (3/2) R + R, KE change + work. Also Independent of T

Heat Capacity Summary for Ideal Gases: C v = (3/2) R, KE change only. Note, C v independent of T. C p = (3/2) R + R, KE change + work. Also Independent of T C p /C v = [(5/2)R]/[(3/2)R] = 5/3 C p /C v

### Chapter 1. The Properties of Gases Fall Semester Physical Chemistry 1 (CHM2201)

Chapter 1. The Properties of Gases 2011 Fall Semester Physical Chemistry 1 (CHM2201) Contents The Perfect Gas 1.1 The states of gases 1.2 The gas laws Real Gases 1.3 Molecular interactions 1.4 The van

### Temperature and Heat. Ken Intriligator s week 4 lectures, Oct 21, 2013

Temperature and Heat Ken Intriligator s week 4 lectures, Oct 21, 2013 This week s subjects: Temperature and Heat chapter of text. All sections. Thermal properties of Matter chapter. Omit the section there

### Final Review #4 Experiments Statistical Mechanics, Kinetic Theory Ideal Gas Thermodynamics Heat Engines Relativity

Final Review #4 Experiments Statistical Mechanics, Kinetic Theory Ideal Gas Thermodynamics Heat Engines Relativity 8.01t December 8, 2004 Review of 8.01T Experiments Experiment 01: Introduction to DataStudio

### Chapter 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

### FTF Day 9. April 9, 2012 HW: Assessment Questions 13.1 (Wed) Folder Check Quiz on Wednesday Topic: Gas laws Question: What are gasses like?

Gas Laws Ch 13 FTF Day 9 April 9, 2012 HW: Assessment Questions 13.1 (Wed) Folder Check Quiz on Wednesday Topic: Gas laws Question: What are gasses like? Describe motion of particles, compressibility,

### Kinetic Theory of Gases

EDR = Engel, Drobny, Reid, Physical Chemistry for the Life Sciences text Kinetic Theory of Gases Levine Chapter 14 "So many of the properties of [gases]...can be deduced from the hypothesis that their

### Chapter 17 Thermal Expansion and the Gas Laws

So many of the properties of matter, especially when in the gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with the temperature, that

### There are three phases of matter: Solid, liquid and gas

FLUIDS: Gases and Liquids Chapter 4 of text There are three phases of matter: Solid, liquid and gas Solids: Have form, constituents ( atoms and molecules) are in fixed positions (though they can vibrate

### Chapter Practice Test Grosser

Class: Date: Chapter 10-11 Practice Test Grosser Multiple Choice Identify the choice that best completes the statement or answers the question. 1. According to the kinetic-molecular theory, particles of

### Physics 408 Final Exam

Physics 408 Final Exam Name You are graded on your work (with partial credit where it is deserved) so please do not just write down answers with no explanation (or skip important steps)! Please give clear,

### Atoms, electrons and Solids

Atoms, electrons and Solids Shell model of an atom negative electron orbiting a positive nucleus QM tells that to minimize total energy the electrons fill up shells. Each orbit in a shell has a specific

### Properties of Gases. Occupy the entire volume of their container Compressible Flow readily and mix easily Have low densities, low molecular weight

Chapter 5 Gases Properties of Gases Occupy the entire volume of their container Compressible Flow readily and mix easily Have low densities, low molecular weight Atmospheric Pressure Atmospheric pressure

### Some Vocabulary. Chapter 10. Zeroth Law of Thermodynamics. Thermometers

Chapter 0 Some Vocabulary Thermal Physics, Temperature and Heat Thermodynamics: Study of energy transfers (engines) Changes of state (solid, liquid, gas...) Heat: Transfer of microscopic thermal energy

### CY T. Pradeep. Lectures 11 Theories of Reaction Rates

CY1001 2015 T. Pradeep Lectures 11 Theories of Reaction Rates There are two basic theories: Collision theory and activated complex theory (transition state theory). Simplest is the collision theory accounts

### 10/12/10. Chapter 16. A Macroscopic Description of Matter. Chapter 16. A Macroscopic Description of Matter. State Variables.

Chapter 16. A Macroscopic Description of Matter Macroscopic systems are characterized as being either solid, liquid, or gas. These are called the phases of matter, and in this chapter we ll be interested

### KINETIC 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

### EXPERIMENT 3. HEAT-CAPACITY RATIOS FOR GASES

EXERIMENT 3. HEAT-CAACITY RATIOS FOR GASES The ratio Cp/Cv of the heat capacity of a gas at constant pressure to that at constant volume will be determined by either the method of adiabatic expansion.

### Physics 53. Thermal Physics 1. Statistics are like a bikini. What they reveal is suggestive; what they conceal is vital.

Physics 53 Thermal Physics 1 Statistics are like a bikini. What they reveal is suggestive; what they conceal is vital. Arthur Koestler Overview In the following sections we will treat macroscopic systems

### D g << D R < D s. Chapter 10 Gases & Kinetic Molecular Theory. I) Gases, Liquids, Solids Gases Liquids Solids. Particles far apart

Chapter 10 Gases & Kinetic Molecular Theory I) Gases, Liquids, Solids Gases Liquids Solids Particles far apart Particles touching Particles closely packed very compressible slightly comp. Incomp. D g

### van der Waals Isotherms near T c

van der Waals Isotherms near T c v d W loops are not physical. Why? Patch up with Maxwell construction van der Waals Isotherms, T/T c van der Waals Isotherms near T c Look at one of the van der Waals isotherms

### askiitians Class: 11 Subject: Chemistry Topic: Kinetic theory of gases No. of Questions: The unit of universal gas constant in S.I.

Class: 11 Subject: Chemistry Topic: Kinetic theory of gases No. of Questions: 33 1. The unit of universal gas constant in S.I.unit is A. calorie per degree Celsius B. joule per mole C. joule/k mole C 2.

### Thermodynamics. Thermo : heat dynamics : motion Thermodynamics is the study of motion of heat. Time and Causality Engines Properties of matter

Thermodynamics Thermo : heat dynamics : motion Thermodynamics is the study of motion of heat. Time and Causality Engines Properties of matter Graeme Ackland Lecture 1: Systems and state variables September

### Process 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

### Gases. T boil, K. 11 gaseous elements. Rare gases. He, Ne, Ar, Kr, Xe, Rn Diatomic gaseous elements H 2, N 2, O 2, F 2, Cl 2

Gases Gas T boil, K Rare gases 11 gaseous elements He, Ne, Ar, Kr, Xe, Rn 165 Rn 211 N 2 O 2 77 F 2 90 85 Diatomic gaseous elements Cl 2 238 H 2, N 2, O 2, F 2, Cl 2 H 2 He Ne Ar Kr Xe 20 4.4 27 87 120

### Some General Remarks Concerning Heat Capacity

CHEM 331 Physical Chemistry Fall 2017 Some General Remarks Concerning Heat Capacity The Heat Capacity The Heat Capacity is one of those quantities whose role in thermodynamics cannot be underestimated.

### Lecture PowerPoints. Chapter 13 Physics: Principles with Applications, 7 th edition Giancoli

Lecture PowerPoints Chapter 13 Physics: Principles with Applications, 7 th edition Giancoli This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching

### A 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

### S = k log W 11/8/2016 CHEM Thermodynamics. Change in Entropy, S. Entropy, S. Entropy, S S = S 2 -S 1. Entropy is the measure of dispersal.

Entropy is the measure of dispersal. The natural spontaneous direction of any process is toward greater dispersal of matter and of energy. Dispersal of matter: Thermodynamics We analyze the constraints

### Chapter 14 Molecular Model of Matter

Chapter 14 Molecular Model of Matter GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions Define each of the following terms, and use

### CHAPTER 16 A MACROSCOPIC DESCRIPTION OF MATTER

CHAPTER 16 A MACROSCOPIC DESCRIPTION OF MATTER This brief chapter provides an introduction to thermodynamics. The goal is to use phenomenological descriptions of the microscopic details of matter in order

### Honors Physics. Notes Nov 16, 20 Heat. Persans 1

Honors Physics Notes Nov 16, 20 Heat Persans 1 Properties of solids Persans 2 Persans 3 Vibrations of atoms in crystalline solids Assuming only nearest neighbor interactions (+Hooke's law) F = C( u! u

### Chapter 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

### Chapter 5. Gases and the Kinetic-Molecular Theory

Chapter 5 Gases and the Kinetic-Molecular Theory Macroscopic vs. Microscopic Representation Kinetic Molecular Theory of Gases 1. Gas molecules are in constant motion in random directions. Collisions among

### Thermal & Statistical Physics Study Questions for the Spring 2018 Department Exam December 6, 2017

Thermal & Statistical Physics Study Questions for the Spring 018 Department Exam December 6, 017 1. a. Define the chemical potential. Show that two systems are in diffusive equilibrium if 1. You may start

### Warning!! Chapter 5 Gases. Chapter Objectives. Chapter Objectives. Chapter Objectives. Air Pollution

Warning!! Larry Brown Tom Holme www.cengage.com/chemistry/brown Chapter 5 Gases These slides contains visual aids for learning BUT they are NOT the actual lecture notes! Failure to attend to lectures most

### Thermal and Statistical Physics Department Exam Last updated November 4, L π

Thermal and Statistical Physics Department Exam Last updated November 4, 013 1. a. Define the chemical potential µ. Show that two systems are in diffusive equilibrium if µ 1 =µ. You may start with F =

### Chapter 6: Gases. Philip Dutton University of Windsor, Canada N9B 3P4. Prentice-Hall 2002

General Chemistry Principles and Modern Applications Petrucci Harwood Herring 8 th Edition Chapter 6: Gases Philip Dutton University of Windsor, Canada N9B 3P4 Prentice-Hall 2002 Prentice-Hall 2002 General

### MP203 Statistical and Thermal Physics. Jon-Ivar Skullerud and James Smith

MP203 Statistical and Thermal Physics Jon-Ivar Skullerud and James Smith December 20, 2017 1 Contents 1 Introduction 4 1.1 Temperature and thermal equilibrium.................... 5 1.1.1 The zeroth law

### Protein dynamics. Folding/unfolding dynamics. Fluctuations near the folded state

Protein dynamics Folding/unfolding dynamics Passage over one or more energy barriers Transitions between infinitely many conformations B. Ozkan, K.A. Dill & I. Bahar, Protein Sci. 11, 1958-1970, 2002 Fluctuations

### Solutions Midterm Exam 3 December 12, Match the above shown players of the best baseball team in the world with the following names:

Problem 1 (2.5 points) 1 2 3 4 Match the above shown players of the best baseball team in the world with the following names: A. Derek Jeter B. Mariano Rivera C. Johnny Damon D. Jorge Posada 1234 = a.

### density (in g/l) = molar mass in grams / molar volume in liters (i.e., 22.4 L)

Unit 9: The Gas Laws 9.5 1. Write the formula for the density of any gas at STP. Name: KEY Text Questions from Corwin density (in g/l) = molar mass in grams / molar volume in liters (i.e., 22.4 L) Ch.

### Chapter 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

### Unit 6. Unit Vocabulary: Distinguish between the three phases of matter by identifying their different

*STUDENT* Unit Objectives: Absolute Zero Avogadro s Law Normal Boiling Point Compound Cooling Curve Deposition Energy Element Evaporation Heat Heat of Fusion Heat of Vaporization Unit 6 Unit Vocabulary:

### CHEMISTRY NOTES Chapter 12. The Behavior of Gases

Goals : To gain an understanding of : 1. The kinetic theory of matter. 2. Avogadro's hypothesis. 3. The behavior of gases and the gas laws. NOTES: CHEMISTRY NOTES Chapter 12 The Behavior of Gases The kinetic

### Physics 123 Unit #2 Review

Physics 123 Unit #2 Review I. Definitions & Facts thermal equilibrium ideal gas thermal energy internal energy heat flow heat capacity specific heat heat of fusion heat of vaporization phase change expansion

### Hood River Valley High

Chemistry Hood River Valley High Name: Period: Unit 7 States of Matter and the Behavior of Gases Unit Goals- As you work through this unit, you should be able to: 1. Describe, at the molecular level, the

### Brownian Motion and The Atomic Theory

Brownian Motion and The Atomic Theory Albert Einstein Annus Mirabilis Centenary Lecture Simeon Hellerman Institute for Advanced Study, 5/20/2005 Founders Day 1 1. What phenomenon did Einstein explain?

### IMPACT Today s Objectives: In-Class Activities:

Today s Objectives: Students will be able to: 1. Understand and analyze the mechanics of impact. 2. Analyze the motion of bodies undergoing a collision, in both central and oblique cases of impact. IMPACT

### Summary of Gas Laws V T. Boyle s Law (T and n constant) Charles Law (p and n constant) Combined Gas Law (n constant) 1 =

Summary of Gas Laws Boyle s Law (T and n constant) p 1 V 1 = p 2 V 2 Charles Law (p and n constant) V 1 = T 1 V T 2 2 Combined Gas Law (n constant) pv 1 T 1 1 = pv 2 T 2 2 1 Ideal Gas Equation pv = nrt

### Ch 6 Gases 6 GASES. Property of gases. pressure = force/area

6 GASES Gases are one of the three states of matter, and while this state is indispensable for chemistry's study of matter, this chapter mainly considers the relationships between volume, temperature and

### Physics, Chapter 16: Kinetic Theory of Gases

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1958 Physics, Chapter 16: Kinetic Theory of Gases Henry

### Estimate, for this water, the specific heat capacity, specific heat capacity =... J kg 1 K 1. the specific latent heat of vaporisation.

1 A kettle is rated as 2.3 kw. A mass of 750 g of water at 20 C is poured into the kettle. When the kettle is switched on, it takes 2.0 minutes for the water to start boiling. In a further 7.0 minutes,

### Gases and the Kinetic Molecular Theory

Gases and the Kinetic olecular Theory Importance in atmospheric phenomena, gas phase reactions, combustion engines, etc. 5.1 The hysical States of atter The condensed states liquid and solid The gaseous

### 1 Energy is supplied to a fixed mass of gas in a container and the absolute temperature of the gas doubles.

1 Energy is supplied to a fixed mass of gas in a container and the absolute temperature of the gas doubles. The mean square speed of the gas molecules A remains constant. B increases by a factor of 2.

Dr. Fritz Wilhelm page of C:\physics\3 lecture\ch9 temperature ideal gas law.docx; Last saved: /5/ 6:46: PM; Last printed:/5/ 6:46: PM Problems: See website, Table of Contents: 9. Temperature as a Measure

### SCH 3UI Unit 08 Outline: Kinetic Molecular Theory and the Gas Laws. The States of Matter Characteristics of. Solids, Liquids and Gases

SCH 3UI Unit 08 Outline: Kinetic Molecular Theory and the Gas Laws Lesson Topics Covered Handouts to Print 1 Note: The States of Matter solids, liquids and gases state and the polarity of molecules the

### The Gas Laws. Types of Variation. What type of variation is it? Write the equation of the line.

The Gas Laws 1) Types of Variation 2) Boyle's Law + P V Investigation 3) Charles' Law + T V Thought Lab 4) Lussac's Law + T P Investigation 5) The Combined Gas Law 6) Avogadro and the Universal Gas Law

### A Gas Uniformly fills any container. Easily compressed. Mixes completely with any other gas. Exerts pressure on its surroundings.

Chapter 5 Gases Chapter 5 A Gas Uniformly fills any container. Easily compressed. Mixes completely with any other gas. Exerts pressure on its surroundings. Copyright Cengage Learning. All rights reserved

### The Gas Laws. Section 1.2 (7th and 8th editions) Individual Gases Boyle s Law Charles Law. Perfect (Ideal) Gas Equation

The Gas Laws Section 1.2 (7th and 8th editions) Individual Gases Boyle s Law Charles Law Perfect (Ideal) Gas Equation Mixtures of Gases Dalton s Law Mole Fractions Last updated: Sept. 14, 2009; minor edits

### Unit Outline. I. Introduction II. Gas Pressure III. Gas Laws IV. Gas Law Problems V. Kinetic-Molecular Theory of Gases VI.

Unit 10: Gases Unit Outline I. Introduction II. Gas Pressure III. Gas Laws IV. Gas Law Problems V. Kinetic-Molecular Theory of Gases VI. Real Gases I. Opening thoughts Have you ever: Seen a hot air balloon?

### Where are we going? Chem Lecture resources. Gases. Charles Law. Boyle s Law. A/Prof Sébastien Perrier. Login: chem1101 Password: carbon12

Chem 1101 Where are we going? examinable A/Prof Sébastien Perrier Room: 351 Phone: 9351-3366 Email: s.perrier@chem.usyd.edu.au Prof Scott Kable Room: 311 Phone: 9351-2756 Email: s.kable@chem.usyd.edu.au