A Gas Law And Absolute Zero

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "A Gas Law And Absolute Zero"

Transcription

1 A Gas Law And Absolute Zero Equipent safety goggles, DataStudio, gas bulb with pressure gauge, 10 C to +110 C theroeter, 100 C to +50 C theroeter. Caution This experient deals with aterials that are very hot and very cold. Exercise care when handling these aterials. Do not let the get in contact with your skin or clothes. Wear safety goggles to protect your eyes fro splashes. 1 Purpose To investigate how the pressure of a given quantity of gas in a fixed volue varies with the teperature. This relationship between pressure and teperature, which is approxiately linear for low nuber densities and teperatures soewhat above liquefaction, is extrapolated to zero pressure. The teperature at which this occurs is absolute zero. 2 Description See Fig. 1. A steel bulb is filled with air at abient air pressure. The bulb is fitted with a pressure gauge that gives the absolute pressure inside the bulb in lb/in 2. When the valve is opened, the pressure gauge gives the noinal outside air pressure, about 15 lb/in 2. With the valve closed the bulb is inserted into 4 liquids of different teperatures. For each liquid, the teperature and pressure are easured. There are 5 pairs of pressure and teperature easureents. These are plotted on a graph and the best straight line is drawn. The straight line is extrapolated to zero pressure. The teperature at that point is deterined and is absolute zero. 3 Theory In an ideal gas the olecules are considered so sall that they can be approxiated as point asses. For siplicity, we let the ter olecules also include atos. It is assued that there are no forces between the olecules and that the energy of the gas is entirely the kinetic energy of the olecules. The olecules are in constant otion and as they bounce off the walls of the container exert a pressure (a force per unit area) on the walls of the container. On a very short tie scale the pressure fluctuates a great deal, but on a longer tie scale the pressure fluctuations average out. The average kinetic energy of the olecules increases with the teperature, and the higher the teperature the faster the olecules ove. The pressure exerted by the gas will increase as the teperature rises because the olecules ove faster and hit the wall harder and ore often. It is found that the pressure p and Teperature T C obey a linear relationship that can be written as p = T C + b, (1) where and b are constants and T C is the centigrade teperature. 1

2 No gas is strictly ideal and there will be deviations fro Eq.(1), particularly as the gas becoes ore dense and/or the teperature is decreased. But for dilute gases at high enough teperatures this equation is a good approxiation. As the teperature decreases ost gases will eventually becoe liquid and Eq.(1) is not valid. If data in the range where Eq.(1) is valid is extrapolated to p = 0, the very low teperature at which this occurs is independent of the gas used and is tered absolute zero. According to Eq.(1) absolute zero occurs at the centigrade teperature T C = b = There is no teperature colder than absolute zero! If the kelvin teperature T is defined as T = T C + b, Eq.(1) can be written as p = T. (2) What should the constant be, and is it a constant for all situations? Following is a rough derivation. Let the nuber density (nuber of olecules per unit volue) of the gas olecules be n N. The nuber of olecules striking per unit area of the container wall per unit tie is n N v, where v is a suitable average speed of the olecules. The oentu carried by each olecule is proportional to Mv, where M is the ass of the olecule. The oentu carried toward the wall per unit area per unit tie is proportional to n N Mv 2, and the oentu carried away fro the wall per unit area per unit tie the sae value. The net oentu transferred to the wall per unit area per unit tie will be proportional to 2n N Mv 2, and according to Newton s 2nd law, is proportional to the pressure. But Mv 2 is proportional to the kinetic energy which in turn, according to kinetic theory, is proportional to the Kelvin teperature. We ust have that the pressure is proportional to the product of the n N and T, or p = n N kt, (3) where k is the proportionality constant and is called Boltzann s constant. For Eq.(3) to be written in this siple for without an additive constant on the right hand side, the teperature ust be in kelvin. Note that one degree kelvin is equal to one degree centigrade. Let the volue of the gas be V and Avogadro s nuber be N A. If both the nuerator and denoinator of the right hand side of Eq.(3) are ultiplied by V and N A, this equation can be written P V = nrt, (4) where n is the nuber of oles of the gas and N A k = R = 8.31 J/ole/K is the gas constant. It is custoary to write K for degrees kelvin rather than K or deg K. 4 Experient Wear safety goggles to protect your eyes fro splashes. 1. Begin by depressing the pin inside the end of the valve attached to the bulb. This connects the bulb to the roo air and sets the bulb pressure at one atosphere. Do not open the valve again. Record the value indicated by the pressure gauge in units of lb/in 2, tapping the gauge gently with a fingernail to be sure that the needle is not sticking (a good procedure with any echanical gauge). Record also the teperature 2

3 in the roo using the 10 C to +110 C theroeter. Be careful that your hand does not war the bulb above roo teperature. 2. Ierse the bulb in boiling water. Use the 10 C to +110 C theroeter to easure the teperature of the water. Do not let the theroeter touch the botto or sides of the boiling water container, where the teperature ay differ fro that of the water. When equilibriu is reached (the pressure reading becoes constant), record the pressure and the teperature. Reove the bulb fro the stea bath and allow it to reach roo teperature. Check to see that the pressure reading is the sae as it was before subjecting the gas to the boiling water. If it is significantly different you ay have a leak. 3. Ierse the bulb in a water-ice ixture. Using the sae procedures as before, easure the pressure and teperature using the sae theroeter. 4. Note: In this part of the experient, do not use the sae theroeter. You will break it. Use the 100 C to +50 C theroeter. Ierse the bulb and a suitable theroeter in alcohol. At first cool the alcohol by adding sall chips of solid carbon dioxide. Do not touch the chips with unprotected fingers! As the teperature drops and the boiling becoes less violent add larger pieces of the carbon dioxide. It should be possible to lower the teperature to about 72 C. Record the pressure and teperature as before. 5. In this part of the experient, do not insert any theroeter as it will break. Ierse the bulb in liquid nitrogen. Do this slowly to iniize violent boiling. Take care not to touch the liquid nitrogen or to be splashed by it. Assue the teperature is 196 C. Allow the gas to reach equilibriu and record the pressure. 6. When the bulb returns to roo teperature check to see if it returns to about its original pressure. 5 Data Analysis Analyze your data by plotting it on a DataStudio graph display and fitting a straight line to the data points. This is a least squares fit. As the horizontal axis of the graph display will not accept negative nubers, it is necessary to rewrite Eq.(1) as T = 1 p b. (5) The teperature T will be plotted on the vertical axis and the pressure p on the horizontal axis. The slope of the line is 1 and the vertical axis intercept (when p = 0) is b, which is the value of absolute zero. To plot your data and find the slope and vertical axis intercept You re required to. 1. Open New Epty Data Table by selecting it fro Experient on the enu bar. 2. Enter your 5 pairs of data points in the x and y coluns. 3. Drag the Graph icon fro the Displays enu to the Data that you just input in the Data enu. The horizontal axis will be islabeled x but the nubers will be right. 3

4 4. Click the statistics button at the top of the graph window. Reeber to resize either axis you, double click on the graph to get Graph Settings. After click on the axis settings tab. Once here you can input the axiu and iniu values. On the horizontal axis ake ax a nuber slightly larger than your axiu recorded pressure and leave in at 0. On the vertical axis ake ax 110 and ake in All 5 of your data points should be visible in the graph window. 5. Ath the top of the graph window there is a Fit button, click it and then choose linear. The least squares straight line fit will appear through your data points. Print out the required nuber of graphs, cross out Tie(s) below the horizontal axis and enter Pressure lb/in Obtain values for and b. In doing so, give units. Consider the following questions. 6 Results What are the diensions of teperature? List the units of teperature that you know. What are the diensions of and b? What units of and b are you using? Hint: They are not the sae. Discuss your results. Suggestions. How well do your data fit a straight line? What is your value for absolute zero in degrees centigrade ( b )? Do the units ake sense? Since Boltzann s constant k = J/K, what is n N for your experient? Hint: k is given in S.I. units. Express in S.I. units, and calculate the density in olecules per cubic eter. Envision, if you can, that nuber of olecules. The diaeter of the bulb is about 10 c. Neglecting the wall thickness of the bulb, and the volue of the connecting tubing and pressure gauge, about how any oles of air are you working with? One of the assuptions in your data analysis is that the density of the air in the bulb stays constant. How any reasons can you think of for this not to be so? What kind of errors ight be introduced? Exercise. Obtain Eq.(4) fro Eq.(3). 4

5 7 Coent You ight think that at zero degrees Kelvin atoic and olecular otion ceases. This is not the case. There is still a little bit of otion to these particles at absolute zero which is called zero point energy. One of the stateents of the Heisenberg uncertainty principle of quantu echanics is that for each linear diension the product of the uncertainties in oentu and position of a particle ust be greater than or equal to Planck s constant h divided by 2π or h/2π. For exaple, if the linear diension is denoted by x and the uncertainties in position and oentu are denoted by x and p x, then x p x. If the oentu were zero (no otion) its oentu would be known exactly (no uncertainty, p x = 0) and we would have no idea where the particle was. 8 Finishing Up Please leave your bench as you found it. Thank you. Figure 1: Fixed voloue of gas in a constant teperature bath. 5

A Gas Law And Absolute Zero Lab 11

A Gas Law And Absolute Zero Lab 11 HB 04-06-05 A Gas Law And Absolute Zero Lab 11 1 A Gas Law And Absolute Zero Lab 11 Equipent safety goggles, SWS, gas bulb with pressure gauge, 10 C to +110 C theroeter, 100 C to +50 C theroeter. Caution

More information

( C) CLASS 10. TEMPERATURE AND ATOMS

( C) CLASS 10. TEMPERATURE AND ATOMS CLASS 10. EMPERAURE AND AOMS 10.1. INRODUCION Boyle s understanding of the pressure-volue relationship for gases occurred in the late 1600 s. he relationships between volue and teperature, and between

More information

HW 2. Q v. kt Step 1: Calculate N using one of two equivalent methods. Problem 4.2. a. To Find:

HW 2. Q v. kt Step 1: Calculate N using one of two equivalent methods. Problem 4.2. a. To Find: HW 2 Proble 4.2 a. To Find: Nuber of vacancies per cubic eter at a given teperature. b. Given: T 850 degrees C 1123 K Q v 1.08 ev/ato Density of Fe ( ρ ) 7.65 g/cc Fe toic weight of iron ( c. ssuptions:

More information

The Velocities of Gas Molecules

The Velocities of Gas Molecules he Velocities of Gas Molecules by Flick Colean Departent of Cheistry Wellesley College Wellesley MA 8 Copyright Flick Colean 996 All rights reserved You are welcoe to use this docuent in your own classes

More information

COMMON SYSTEMS OF MEASUREMENTS

COMMON SYSTEMS OF MEASUREMENTS 31 SI Units CHAPTER CONTENTS COMMON SYSTEMS OF MEASUREMENTS (1) Metric Syste (2) SI Syste SI UNIT OF LENGTH SI UNIT OF VOLUME SI UNIT OF TEMPERATURE UNITS OF MASS AND WEIGHT UNITS OF FORCE UNITS OF WORK

More information

Physics 211: Lab Oscillations. Simple Harmonic Motion.

Physics 211: Lab Oscillations. Simple Harmonic Motion. Physics 11: Lab Oscillations. Siple Haronic Motion. Reading Assignent: Chapter 15 Introduction: As we learned in class, physical systes will undergo an oscillatory otion, when displaced fro a stable equilibriu.

More information

IDEAL AND NON-IDEAL GASES

IDEAL AND NON-IDEAL GASES 2/2016 ideal gas 1/8 IDEAL AND NON-IDEAL GASES PURPOSE: To measure how the pressure of a low-density gas varies with temperature, to determine the absolute zero of temperature by making a linear fit to

More information

Kinetic Molecular Theory of Ideal Gases

Kinetic Molecular Theory of Ideal Gases ecture /. Kinetic olecular Theory of Ideal Gases ast ecture. IG is a purely epirical law - solely the consequence of eperiental obserations Eplains the behaior of gases oer a liited range of conditions.

More information

Lecture L9 - Linear Impulse and Momentum. Collisions

Lecture L9 - Linear Impulse and Momentum. Collisions J. Peraire, S. Widnall 16.07 Dynaics Fall 009 Version.0 Lecture L9 - Linear Ipulse and Moentu. Collisions In this lecture, we will consider the equations that result fro integrating Newton s second law,

More information

Electric Forces between Charged Plates

Electric Forces between Charged Plates CP.1 Goals of this lab Electric Forces between Charged Plates Overview deterine the force between charged parallel plates easure the perittivity of the vacuu (ε 0 ) In this experient you will easure the

More information

Lesson 44: Acceleration, Velocity, and Period in SHM

Lesson 44: Acceleration, Velocity, and Period in SHM Lesson 44: Acceleration, Velocity, and Period in SHM Since there is a restoring force acting on objects in SHM it akes sense that the object will accelerate. In Physics 20 you are only required to explain

More information

Chapter 21. The Kinetic Theory of Gases

Chapter 21. The Kinetic Theory of Gases Chapter The Kinetic Theory of Gases CHAPTER OUTLINE. Molecular Model of an Ideal Gas. Molar Specific Heat of an Ideal Gas.3 Adiabatic Processes for an Ideal Gas.4 The Equipartition of Energy.5 The Boltzann

More information

Mh1: Simple Harmonic Motion. Chapter 15. Motion of a Spring-Mass System. Periodic Motion. Oscillatory Motion

Mh1: Simple Harmonic Motion. Chapter 15. Motion of a Spring-Mass System. Periodic Motion. Oscillatory Motion Mh1: Siple Haronic Motion Chapter 15 Siple block and spring Oscillatory Motion Exaple: the tides, a swing Professor Michael Burton School of Physics, UNSW Periodic Motion! Periodic otion is otion of an

More information

The Kinetic Model of Gases

The Kinetic Model of Gases Franziska Hofann, Stephan Steinann February 0, 2007 The Kinetic Model of Gases Introduction The rando otion of perfect gases can be described by kinetic theory. Based on a siple odel pressure, igration,

More information

Kinetic Theory & Ideal Gas

Kinetic Theory & Ideal Gas 1 of 6 Thermodynamics Summer 2006 Kinetic Theory & Ideal Gas The study of thermodynamics usually starts with the concepts of temperature and heat, and most people feel that the temperature of an object

More information

Measurement of radiation. Chapter 7 Measurement of Radiation: Dosimetry. Description of radiation beam. Energy transfer.

Measurement of radiation. Chapter 7 Measurement of Radiation: Dosimetry. Description of radiation beam. Energy transfer. Chapter 7 Measureent of Radiation: osietry Radiation osietry I Text: H.E Johns and J.R. Cunningha, The physics of radiology, 4 th ed. http://www.utoledo.edu/ed/depts/radther Measureent of radiation escription

More information

Lecture 09 Nuclear Physics Part 1

Lecture 09 Nuclear Physics Part 1 Lecture 09 Nuclear Physics Part 1 Structure and Size of the Nucleus Νuclear Masses Binding Energy The Strong Nuclear Force Structure of the Nucleus Discovered by Rutherford, Geiger and Marsden in 1909

More information

2. METRIC SYSTEM AND MEASUREMENT Measuring the world around you

2. METRIC SYSTEM AND MEASUREMENT Measuring the world around you 2. METRI SYSTEM AND MEASUREMENT Measuring the world around you OBJETIVES Figure 2.1 Standard units of the etric syste At the end of this lab, you should be able to: Measure Unit Exaple 1. Identify the

More information

Vectors & Newton's Laws I

Vectors & Newton's Laws I Physics 6 Vectors & Newton's Laws I Introduction In this laboratory you will eplore a few aspects of Newton s Laws ug a force table in Part I and in Part II, force sensors and DataStudio. By establishing

More information

The Mathematics of Pumping Water

The Mathematics of Pumping Water The Matheatics of Puping Water AECOM Design Build Civil, Mechanical Engineering INTRODUCTION Please observe the conversion of units in calculations throughout this exeplar. In any puping syste, the role

More information

Answer, Key Homework 7 David McIntyre 45123 Mar 25, 2004 1

Answer, Key Homework 7 David McIntyre 45123 Mar 25, 2004 1 Answer, Key Hoework 7 David McIntyre 453 Mar 5, 004 This print-out should have 4 questions. Multiple-choice questions ay continue on the next colun or page find all choices before aking your selection.

More information

CHAPTER 7 FLUIDS M V

CHAPTER 7 FLUIDS M V CHPTER 7 LUIDS 7. Density and Pressure The density of an object of total ass M and volue V is defined as ass per unit volue and is given by: ass volue M V SI units : kg/ (g/c ); ( g/c =000 kg/ ) eg: ρ

More information

Gas Thermometer and Absolute Zero

Gas Thermometer and Absolute Zero Chapter 1 Gas Thermometer and Absolute Zero Name: Lab Partner: Section: 1.1 Purpose Construct a temperature scale and determine absolute zero temperature (the temperature at which molecular motion ceases).

More information

4.3 The Graph of a Rational Function

4.3 The Graph of a Rational Function 4.3 The Graph of a Rational Function Section 4.3 Notes Page EXAMPLE: Find the intercepts, asyptotes, and graph of + y =. 9 First we will find the -intercept by setting the top equal to zero: + = 0 so =

More information

Pressure -Temperature Relationship in Gases. Evaluation copy. Figure 1. 125 ml Erlenmeyer flask. Vernier computer interface

Pressure -Temperature Relationship in Gases. Evaluation copy. Figure 1. 125 ml Erlenmeyer flask. Vernier computer interface Pressure -Temperature Relationship in Gases Computer 7 Gases are made up of molecules that are in constant motion and exert pressure when they collide with the walls of their container. The velocity and

More information

Home Work Solutions 12

Home Work Solutions 12 Hoe Work Solutions 1 1-1 In Fig.1, an electric field is directed out of the page within a circular region of radius R =. c. The field agnitude is E = (.5 V/ s)(1 - r/r)t, where t is in seconds and r is

More information

) 1/2 ( J / K 298K. CHEM 4641 Physical Chemistry I Chapter 16 (long-book chapter 33) Recommended Problems

) 1/2 ( J / K 298K. CHEM 4641 Physical Chemistry I Chapter 16 (long-book chapter 33) Recommended Problems CHEM 4641 hysical Cheistry I Chapter 16 (long-book chapter 33) Recoended robles Chapter 16 (33) roble 1 Maxwell speed distribution in two diensions The velocity distribution is siply the Maxwell-Boltzann

More information

Work, Energy, Conservation of Energy

Work, Energy, Conservation of Energy This test covers Work, echanical energy, kinetic energy, potential energy (gravitational and elastic), Hooke s Law, Conservation of Energy, heat energy, conservative and non-conservative forces, with soe

More information

Although born in Bordeaux, France,

Although born in Bordeaux, France, Revisiting Black s Experients on the Latent Heats of Water J. Güéez Departaento de Física Aplicada Universidad de Cantabria E-39005 Santander Spain; gueezj@unican.es C. Fiolhais and M. Fiolhais Departaento

More information

Force. Net Force Mass. Acceleration = Section 1: Weight. Equipment Needed Qty Equipment Needed Qty Force Sensor 1 Mass and Hanger Set 1 Balance 1

Force. Net Force Mass. Acceleration = Section 1: Weight. Equipment Needed Qty Equipment Needed Qty Force Sensor 1 Mass and Hanger Set 1 Balance 1 Department of Physics and Geology Background orce Physical Science 1421 A force is a vector quantity capable of producing motion or a change in motion. In the SI unit system, the unit of force is the Newton

More information

The rate of heat transfer from the condensing steam to the cooling water is given by. (h 4 h 3 )

The rate of heat transfer from the condensing steam to the cooling water is given by. (h 4 h 3 ) Capter 4 Exaple 4.4-6. ---------------------------------------------------------------------------------- Stea enters te condenser of a vapor power plant at 0. bar wit a quality of 0.95 and condensate

More information

! Thermodynamics worked examples

! Thermodynamics worked examples ! Therodynaics worked exaples Refrigeration. (a) What pressure is required in a freezer copartent evaporator coil using refrigerant R34a if the teperature is to be aintained at 0 C? (b) What is the enthalpy

More information

Acceleration of Gravity Lab Basic Version

Acceleration of Gravity Lab Basic Version Acceleration of Gravity Lab Basic Version In this lab you will explore the motion of falling objects. As an object begins to fall, it moves faster and faster (its velocity increases) due to the acceleration

More information

Simple Harmonic Motion MC Review KEY

Simple Harmonic Motion MC Review KEY Siple Haronic Motion MC Review EY. A block attache to an ieal sprin uneroes siple haronic otion. The acceleration of the block has its axiu anitue at the point where: a. the spee is the axiu. b. the potential

More information

Chapter 8: Newton s Third law

Chapter 8: Newton s Third law Warning: My approach is a soewhat abbreviated and siplified version of what is in the text, yet just as coplete. Both y treatent and the text s will prepare you to solve the sae probles. Restating Newton

More information

Internet Electronic Journal of Molecular Design

Internet Electronic Journal of Molecular Design ISSN 1538 6414 Internet Electronic Journal of Molecular Design June 2003, Volue 2, Nuber 6, Pages 375 382 Editor: Ovidiu Ivanciuc Special issue dedicated to Professor Haruo Hosoya on the occasion of the

More information

11 - KINETIC THEORY OF GASES Page 1

11 - KINETIC THEORY OF GASES Page 1 - KIETIC THEORY OF GASES Page Introduction The constituent partices of the atter ike atos, oecues or ions are in continuous otion. In soids, the partices are very cose and osciate about their ean positions.

More information

8. Spring design. Introduction. Helical Compression springs. Fig 8.1 Common Types of Springs. Fig 8.1 Common Types of Springs

8. Spring design. Introduction. Helical Compression springs. Fig 8.1 Common Types of Springs. Fig 8.1 Common Types of Springs Objectives 8. Spring design Identify, describe, and understand principles of several types of springs including helical copression springs, helical extension springs,, torsion tubes, and leaf spring systes.

More information

Combined pool of artefacts maintained by the BIPM and NMIs with primary realizations of the kilogram: Advantages and Difficulties

Combined pool of artefacts maintained by the BIPM and NMIs with primary realizations of the kilogram: Advantages and Difficulties Bureau International des Poids et Mesures CCM Workshop on the ise en pratique of the new definition of the kilogra Noveber 2012 Cobined pool of artefacts aintained by the BIPM and NMIs with priary realizations

More information

Experiment 2 Index of refraction of an unknown liquid --- Abbe Refractometer

Experiment 2 Index of refraction of an unknown liquid --- Abbe Refractometer Experient Index of refraction of an unknown liquid --- Abbe Refractoeter Principle: The value n ay be written in the for sin ( δ +θ ) n =. θ sin This relation provides us with one or the standard ethods

More information

Chapter 13 Simple Harmonic Motion

Chapter 13 Simple Harmonic Motion We are to adit no ore causes of natural things than such as are both true and sufficient to explain their appearances. Isaac Newton 13.1 Introduction to Periodic Motion Periodic otion is any otion that

More information

Semi-invariants IMOTC 2013 Simple semi-invariants

Semi-invariants IMOTC 2013 Simple semi-invariants Sei-invariants IMOTC 2013 Siple sei-invariants These are soe notes (written by Tejaswi Navilarekallu) used at the International Matheatical Olypiad Training Cap (IMOTC) 2013 held in Mubai during April-May,

More information

Answer: Same magnitude total momentum in both situations.

Answer: Same magnitude total momentum in both situations. Page 1 of 9 CTP-1. In which situation is the agnitude of the total oentu the largest? A) Situation I has larger total oentu B) Situation II C) Sae agnitude total oentu in both situations. I: v 2 (rest)

More information

Lab 8: Ballistic Pendulum

Lab 8: Ballistic Pendulum Lab 8: Ballistic Pendulum Equipment: Ballistic pendulum apparatus, 2 meter ruler, 30 cm ruler, blank paper, carbon paper, masking tape, scale. Caution In this experiment a steel ball is projected horizontally

More information

Lab 7: Rotational Motion

Lab 7: Rotational Motion Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125

More information

ChE 203 - Physicochemical Systems Laboratory EXPERIMENT 2: SURFACE TENSION

ChE 203 - Physicochemical Systems Laboratory EXPERIMENT 2: SURFACE TENSION ChE 203 - Physicocheical Systes Laboratory EXPERIMENT 2: SURFACE TENSION Before the experient: Read the booklet carefully. Be aware of the safety issues. Object To deterine the surface tension of water

More information

Lecture L26-3D Rigid Body Dynamics: The Inertia Tensor

Lecture L26-3D Rigid Body Dynamics: The Inertia Tensor J. Peraire, S. Widnall 16.07 Dynaics Fall 008 Lecture L6-3D Rigid Body Dynaics: The Inertia Tensor Version.1 In this lecture, we will derive an expression for the angular oentu of a 3D rigid body. We shall

More information

HOMEWORK #9 MAGNETIC FIELD, ELECTROMAGNETIC INDUCTION, CHAPTER 27

HOMEWORK #9 MAGNETIC FIELD, ELECTROMAGNETIC INDUCTION, CHAPTER 27 HOEWORK #9 AGNETC FELD, ELECTROAGNETC NDUCTON, CHAPTER 7 54 A long tungsten-core solenoid carries a current. (a) f the core is reoved while the current is held constant, does the agnetic field strength

More information

Thermodynamics. Theory: We can summarize the four laws of thermodynamics as follows:

Thermodynamics. Theory: We can summarize the four laws of thermodynamics as follows: 1 Thermodynamics Objective: To investigate the zeroth and first laws of thermodynamics. To calculate properties such as specific heat. To investigate the ideal gas law. To become familiar with basic P-V

More information

Lesson 13: Voltage in a Uniform Field

Lesson 13: Voltage in a Uniform Field Lesson 13: Voltage in a Unifor Field Most of the tie if we are doing experients with electric fields, we use parallel plates to ensure that the field is unifor (the sae everywhere). This carries over to

More information

ENZYME KINETICS: THEORY. A. Introduction

ENZYME KINETICS: THEORY. A. Introduction ENZYME INETICS: THEORY A. Introduction Enzyes are protein olecules coposed of aino acids and are anufactured by the living cell. These olecules provide energy for the organis by catalyzing various biocheical

More information

Meadowlark Optics LCPM-3000 Liquid Crystal Polarimeter Application Note: Determination of Retardance by Polarimetry Tommy Drouillard

Meadowlark Optics LCPM-3000 Liquid Crystal Polarimeter Application Note: Determination of Retardance by Polarimetry Tommy Drouillard Meadowlark Optics LCPM- Liquid Crystal Polarieter Application Note: Deterination of Retardance by Polarietry Toy Drouillard 5 Meadowlark Optics, Inc.. Introduction: The iediate purpose of a polarieter

More information

Building a Basic Arrangement

Building a Basic Arrangement 1 Lesson 1: Building a Basic Arrangeent 1 Tutorial There are any ways you can work as you create a song in GarageBand. You can freely ove back and forth between adding loops, recording Real and Software

More information

Version 001 Summer Review #04 tubman (IBII ) 1

Version 001 Summer Review #04 tubman (IBII ) 1 Version 001 Suer Review #04 tuban (IBII20142015) 1 This print-out should have 20 questions. Multiple-choice questions ay continue on the next colun or page find all choices before answering. Conceptual

More information

CHAPTER 12. Gases and the Kinetic-Molecular Theory

CHAPTER 12. Gases and the Kinetic-Molecular Theory CHAPTER 12 Gases and the Kinetic-Molecular Theory 1 Gases vs. Liquids & Solids Gases Weak interactions between molecules Molecules move rapidly Fast diffusion rates Low densities Easy to compress Liquids

More information

EXPERIMENT 16: Charles Law of Gases V vs T

EXPERIMENT 16: Charles Law of Gases V vs T EXPERIMENT 16: Charles Law of Gases V vs T Materials: Thermometer Bunsen burner Ring stand Clamps 600ml beakers (2) Closed-tip syringe Ice Water Objectives 1. To put to work the model to verify Charles

More information

Study the following diagrams of the States of Matter. Label the names of the Changes of State between the different states.

Study the following diagrams of the States of Matter. Label the names of the Changes of State between the different states. Describe the strength of attractive forces between particles. Describe the amount of space between particles. Can the particles in this state be compressed? Do the particles in this state have a definite

More information

Lab 5: Conservation of Energy

Lab 5: Conservation of Energy Lab 5: Conservation of Energy Equipment SWS, 1-meter stick, 2-meter stick, heavy duty bench clamp, 90-cm rod, 40-cm rod, 2 double clamps, brass spring, 100-g mass, 500-g mass with 5-cm cardboard square

More information

PREDICTION OF MILKLINE FILL AND TRANSITION FROM STRATIFIED TO SLUG FLOW

PREDICTION OF MILKLINE FILL AND TRANSITION FROM STRATIFIED TO SLUG FLOW PREDICTION OF MILKLINE FILL AND TRANSITION FROM STRATIFIED TO SLUG FLOW ABSTRACT: by Douglas J. Reineann, Ph.D. Assistant Professor of Agricultural Engineering and Graee A. Mein, Ph.D. Visiting Professor

More information

Chapter 4 The Properties of Gases

Chapter 4 The Properties of Gases Chapter 4 The Properties of Gases Significant Figure Convention At least one extra significant figure is displayed in all intermediate calculations. The final answer is expressed with the correct number

More information

Calculating the Return on Investment (ROI) for DMSMS Management. The Problem with Cost Avoidance

Calculating the Return on Investment (ROI) for DMSMS Management. The Problem with Cost Avoidance Calculating the Return on nvestent () for DMSMS Manageent Peter Sandborn CALCE, Departent of Mechanical Engineering (31) 45-3167 sandborn@calce.ud.edu www.ene.ud.edu/escml/obsolescence.ht October 28, 21

More information

Part 1: Background - Graphing

Part 1: Background - Graphing Department of Physics and Geology Graphing Astronomy 1401 Equipment Needed Qty Computer with Data Studio Software 1 1.1 Graphing Part 1: Background - Graphing In science it is very important to find and

More information

Don t Lose Your Temperature

Don t Lose Your Temperature DON T LOSE YOUR TEMPERATURE Don t Lose Your Temperature Student Instruction Sheet Challenge When the temperature remains constant, how does the pressure of a gas in a rigid container change as the volume

More information

Kinetic Molecular Theory

Kinetic Molecular Theory Kinetic Molecular Theory Particle volume - The volume of an individual gas particle is small compaired to that of its container. Therefore, gas particles are considered to have mass, but no volume. There

More information

Chapter 5. Principles of Unsteady - State Heat Transfer

Chapter 5. Principles of Unsteady - State Heat Transfer Suppleental Material for ransport Process and Separation Process Principles hapter 5 Principles of Unsteady - State Heat ransfer In this chapter, we will study cheical processes where heat transfer is

More information

LIGHTSTICK KINETICS. INTRODUCTION: General background on rate, activation energy, absolute temperature, and graphing.

LIGHTSTICK KINETICS. INTRODUCTION: General background on rate, activation energy, absolute temperature, and graphing. LIGHTSTICK KINETICS From Advancing Science, Gettysburg College INTRODUCTION: General background on rate, activation energy, absolute temperature, and graphing. THE RATE LAW: The rate of a chemical reaction

More information

Introduction to Unit Conversion: the SI

Introduction to Unit Conversion: the SI The Matheatics 11 Copetency Test Introduction to Unit Conversion: the SI In this the next docuent in this series is presented illustrated an effective reliable approach to carryin out unit conversions

More information

The Gas Laws. The effect of adding gas. 4 things. Pressure and the number of molecules are directly related. Page 1

The Gas Laws. The effect of adding gas. 4 things. Pressure and the number of molecules are directly related. Page 1 The Gas Laws Describe HOW gases behave. Can be predicted by the theory. The Kinetic Theory Amount of change can be calculated with mathematical equations. The effect of adding gas. When we blow up a balloon

More information

THE IDEAL GAS LAW AND KINETIC THEORY

THE IDEAL GAS LAW AND KINETIC THEORY Chapter 14 he Ideal Gas Law and Kinetic heory Chapter 14 HE IDEAL GAS LAW AND KINEIC HEORY REIEW Kinetic molecular theory involves the study of matter, particularly gases, as very small particles in constant

More information

Statistical Mechanics, Kinetic Theory Ideal Gas. 8.01t Nov 22, 2004

Statistical Mechanics, Kinetic Theory Ideal Gas. 8.01t Nov 22, 2004 Statistical Mechanics, Kinetic Theory Ideal Gas 8.01t Nov 22, 2004 Statistical Mechanics and Thermodynamics Thermodynamics Old & Fundamental Understanding of Heat (I.e. Steam) Engines Part of Physics Einstein

More information

Moisture transfer (moist air) Csaba Szikra senior research fellow TUB Faculty of Architecture Department of Building Energetics and Services

Moisture transfer (moist air) Csaba Szikra senior research fellow TUB Faculty of Architecture Department of Building Energetics and Services Moisture transfer (oist air) Csaba Szikra senior research fellow TUB Faculty of Architecture Deartent of Building Energetics and Services szikra@egt.be.hu 2010 Psychroetry Moist air Psychroetry involves

More information

F=ma From Problems and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, morin@physics.harvard.edu

F=ma From Problems and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, morin@physics.harvard.edu Chapter 4 F=a Fro Probles and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, orin@physics.harvard.edu 4.1 Introduction Newton s laws In the preceding two chapters, we dealt

More information

An increase in temperature causes an increase in pressure due to more collisions.

An increase in temperature causes an increase in pressure due to more collisions. SESSION 7: KINETIC THEORY OF GASES Key Concepts In this session we will focus on summarising what you need to know about: Kinetic molecular theory Pressure, volume and temperature relationships Properties

More information

Chemistry, The Central Science, 11th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten. Chapter 10 Gases

Chemistry, The Central Science, 11th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten. Chapter 10 Gases Chemistry, The Central Science, 11th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten Chapter 10 Gases A Gas Has neither a definite volume nor shape. Uniformly fills any container.

More information

ELECTRIC SERVO MOTOR EQUATIONS AND TIME CONSTANTS

ELECTRIC SERVO MOTOR EQUATIONS AND TIME CONSTANTS ELECIC SEO MOO EQUAIONS AND IME CONSANS George W. Younkin, P.E. Life FELLOW IEEE Industrial Controls Consulting, Div. Bulls Eye Marketing, Inc Fond du c, Wisconsin In the analysis of electric servo drive

More information

Type: Double Date: Kinetic Energy of an Ideal Gas II. Homework: Read 14.3, Do Concept Q. # (15), Do Problems # (28, 29, 31, 37)

Type: Double Date: Kinetic Energy of an Ideal Gas II. Homework: Read 14.3, Do Concept Q. # (15), Do Problems # (28, 29, 31, 37) Type: Double Date: Objective: Kinetic Energy of an Ideal Gas I Kinetic Energy of an Ideal Gas II Homework: Read 14.3, Do Concept Q. # (15), Do Problems # (8, 9, 31, 37) AP Physics Mr. Mirro Kinetic Energy

More information

Reading: Graphing Techniques Revised 3/6/12 GRAPHING TECHNIQUES

Reading: Graphing Techniques Revised 3/6/12 GRAPHING TECHNIQUES GRAPHING TECHNIQUES Mathematical relationships between variables are determined by graphing experimental data. For example, the linear relationship between the concentration and the absorption of dilute

More information

Homework 8. problems: 10.40, 10.73, 11.55, 12.43

Homework 8. problems: 10.40, 10.73, 11.55, 12.43 Hoework 8 probles: 0.0, 0.7,.55,. Proble 0.0 A block of ass kg an a block of ass 6 kg are connecte by a assless strint over a pulley in the shape of a soli isk having raius R0.5 an ass M0 kg. These blocks

More information

Temperature, Expansion, Ideal Gas Law

Temperature, Expansion, Ideal Gas Law Temperature, Expansion, Ideal Gas Law Physics 1425 Lecture 30 Michael Fowler, UVa Everything s Made of Atoms This idea was only fully accepted about 100 years ago in part because of Einstein s analysis

More information

The Concept of the Effective Mass Tensor in GR. The Equation of Motion

The Concept of the Effective Mass Tensor in GR. The Equation of Motion The Concept of the Effective Mass Tensor in GR The Equation of Motion Mirosław J. Kubiak Zespół Szkół Technicznych, Gruziąz, Polan Abstract: In the papers [, ] we presente the concept of the effective

More information

Symmetry. The primitive lattice vectors are:

Symmetry. The primitive lattice vectors are: Syetry Previously, we noted all crystal structures could be specified by a set of Bravais lattice vectors, when describing a lattice you ust either use the priitive vectors or add a set of basis vectors

More information

Prelab Exercises: Hooke's Law and the Behavior of Springs

Prelab Exercises: Hooke's Law and the Behavior of Springs 59 Prelab Exercises: Hooke's Law and the Behavior of Springs Study the description of the experiment that follows and answer the following questions.. (3 marks) Explain why a mass suspended vertically

More information

A magnetic Rotor to convert vacuum-energy into mechanical energy

A magnetic Rotor to convert vacuum-energy into mechanical energy A agnetic Rotor to convert vacuu-energy into echanical energy Claus W. Turtur, University of Applied Sciences Braunschweig-Wolfenbüttel Abstract Wolfenbüttel, Mai 21 2008 In previous work it was deonstrated,

More information

Salty Waters. Instructions for the activity 3. Results Worksheet 5. Class Results Sheet 7. Teacher Notes 8. Sample results. 12

Salty Waters. Instructions for the activity 3. Results Worksheet 5. Class Results Sheet 7. Teacher Notes 8. Sample results. 12 1 Salty Waters Alost all of the water on Earth is in the for of a solution containing dissolved salts. In this activity students are invited to easure the salinity of a saple of salt water. While carrying

More information

EXCEL EXERCISE AND ACCELERATION DUE TO GRAVITY

EXCEL EXERCISE AND ACCELERATION DUE TO GRAVITY EXCEL EXERCISE AND ACCELERATION DUE TO GRAVITY Objective: To learn how to use the Excel spreadsheet to record your data, calculate values and make graphs. To analyze the data from the Acceleration Due

More information

The Kinetic Theory of Gases Sections Covered in the Text: Chapter 18

The Kinetic Theory of Gases Sections Covered in the Text: Chapter 18 The Kinetic Theory of Gases Sections Covered in the Text: Chapter 18 In Note 15 we reviewed macroscopic properties of matter, in particular, temperature and pressure. Here we see how the temperature and

More information

Simple Harmonic Motion

Simple Harmonic Motion SHM-1 Siple Haronic Motion A pendulu, a ass on a spring, and any other kinds of oscillators ehibit a special kind of oscillatory otion called Siple Haronic Motion (SHM). SHM occurs whenever : i. there

More information

Chapter 5: Work, Power & Energy

Chapter 5: Work, Power & Energy Chapter 5: Work, Power & Energy Abition is like a vector; it needs agnitude and direction. Otherwise, it s just energy. Grace Lindsay Objectives 1. Define work and calculate the work done by a force..

More information

Table of Contents. Graphing with Excel 1

Table of Contents. Graphing with Excel 1 Table of Contents Graphing with Excel 1 1. Graphing Data 1.1. Starting the Chart Wizard 1.2. Selecting the Data 1.3. Selecting the Chart Options 1.3.1. Titles Tab 1.3.2. Axes Tab 1.3.3. Gridlines Tab 1.3.4.

More information

Determination of the Molar Mass of an Unknown Solid by Freezing Point Depression

Determination of the Molar Mass of an Unknown Solid by Freezing Point Depression Determination of the Molar Mass of an Unknown Solid by Freezing Point Depression GOAL AND OVERVIEW In the first part of the lab, a series of solutions will be made in order to determine the freezing point

More information

Process chosen to calculate entropy change for the system

Process chosen to calculate entropy change for the system Chapter 6 Exaple 6.3-3 3. ---------------------------------------------------------------------------------- An insulated tank (V 1.6628 L) is divided into two equal parts by a thin partition. On the left

More information

HEAT OF FUSION MECHANICAL EQUIVALENT OF HEAT AND PART A. HEAT OF FUSION

HEAT OF FUSION MECHANICAL EQUIVALENT OF HEAT AND PART A. HEAT OF FUSION HEAT OF FUSION AND MECHANICAL EQUIVALENT OF HEAT CAUTION: Please handle thermometers gently. Broken mercury-filled thermometers should be taken to Rm. B-31 for disposal as mercury is very toxic. If a red-liquid

More information

and that of the outgoing water is mv f

and that of the outgoing water is mv f Week 6 hoework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign ersions of these probles, arious details hae been changed, so that the answers will coe out differently. The ethod to find the solution is

More information

Name Date: Course number: MAKE SURE TA & TI STAMPS EVERY PAGE BEFORE YOU START EXPERIMENT 9. Superconductivity & Ohm s Law

Name Date: Course number: MAKE SURE TA & TI STAMPS EVERY PAGE BEFORE YOU START EXPERIMENT 9. Superconductivity & Ohm s Law Laboratory Section: Last Revised on January 6, 2016 Partners Names: Grade: EXPERIMENT 9 Superconductivity & Ohm s Law 0. Pre-Laboratory Work [2 pts] 1. Define the critical temperature for a superconducting

More information

Shoe Size Data Investigation

Shoe Size Data Investigation Spring 013 Shoe Size Data Investigation Participants note shoe size rounded to the nearest whole nuber. For ales, add 1.5 and round to the nearest whole nuber, this will equalize the ale/feale size differences.

More information

THE BEHAVIOR OF GASES

THE BEHAVIOR OF GASES 12 THE BEHAVIOR OF GASES Conceptual Curriculum Concrete concepts More abstract concepts or math/problem-solving Standard Curriculum Core content Extension topics Honors Curriculum Core honors content Options

More information

Dealing with Data in Excel 2010

Dealing with Data in Excel 2010 Dealing with Data in Excel 2010 Excel provides the ability to do computations and graphing of data. Here we provide the basics and some advanced capabilities available in Excel that are useful for dealing

More information

SAM Teachers Guide Heat and Temperature

SAM Teachers Guide Heat and Temperature SAM Teachers Guide Heat and Temperature Overview Students learn that temperature measures average kinetic energy, and heat is the transfer of energy from hot systems to cold systems. They consider what

More information

Lecture 24: Spinodal Decomposition: Part 3: kinetics of the

Lecture 24: Spinodal Decomposition: Part 3: kinetics of the Leture 4: Spinodal Deoposition: Part 3: kinetis of the oposition flutuation Today s topis Diffusion kinetis of spinodal deoposition in ters of the onentration (oposition) flutuation as a funtion of tie:

More information

Determination of Molecular Weight by Freezing Point Depression

Determination of Molecular Weight by Freezing Point Depression Determination of Molecular Weight by Freezing Point Depression Freezing point depression is a kind of colligative properties as treated in high school chemistry course. Normally used alcohol or mercury

More information