For narration please double click here SelfPaced Online

For narration please double click here Self-Paced Online iiiii. Physics Instruction by David V. Anderson & Peter Tarsi June 16, 2008 • Replaces Age-Based Group Instruction • Utilizes Automated Tutoring • Provided By Asora’s Stellar Schools • Previewed In Physics with Calculus Example

For narration please double click here Prehistorical Origins of The Instructional Formats Of Tutoring And Group Instruction Tutoring and Group Instruction Predate History Tutoring: Student Centered and Self-Paced Group Instruction: Inexpensive but Teacher Paced

History of Age-Based Group Instruction In a Western Context: In Reformation, Calvin, Luther and Zwingli Advocated For It Soon Sturm Had A School In Strasbourg With Nine Grades In 1537 Pestalozzi Ran School In Burgdorf In 1799 & Advised Prussians Prussian Minister Of Education Von Humboldt Led Reforms In 1809 American Educator Horace Mann And Others Copied Prussian Ideas For narration please double click here

For narration please double click here History of Self-Paced Schoolroom Instruction In a Western Context: Bell And Lancaster Developed The Monitorial Systems Circa 1800 One Teacher Managed Approximately 200 Students Dozens Of Monitors Each Led Small Courses Of Perhaps 10 Pupils Monitors Were Advanced Students Who Were Compensated Poorly Pupils Moved To A New Course When Previous One Was Mastered Age Of Student Was Not A Factor In Placing Child In A Course

Age Based Schooling Thrived While Self Paced Varieties Did Not Many Lancastrian Schools Were Poorly Managed And Overcrowded Most Lancastrian Schools Were Private & Poorly Funded Age Based Schools Were Mostly Government Run & Funded Quality Control Hampered In Both By Lack Of Good Metrics Nearly All Schools Are Age Based Whether Public Or Private The One Room Rural School Has Had Lancastrian Aspects For narration please double click here

William Shearer Developed Pliant Grading Introduced A Form Of Self Pacing Children Were Promoted Or Not Monthly Several Classes Would Occupy Each Schoolroom This excerpt from Shearer’s 1898 book suggests that his system was efficient and effective-but also quite complicated. For narration please double click here

For narration please double click here Age Based Group Instruction Is Seriously Flawed Proficiency Standards And Testing Now Well Developed In The USA The National Assessment Of Education Progress (NAEP) Is The Tool Only 30% Of American ~13 -Yr Olds Are Proficient In Math & Science Recent Research Mapped TIMSS And PISA Proficiencies Onto NAEP English Speaking Western World Has ~30% Of 13 -Yr Olds Proficient Continental European Countries Have ~40% Of 13 -Yr Olds Proficient The Better Asian Countries Have ~50% Of 13 -Yr Olds Proficient

For narration please double click here Social Promotion Is Cause Of Low Proficiencies Social Promotion Is The Promoting Of Sub-Proficient Students Historically, Retention Has Been The Remedy For Low Proficiences Draconian Aspects Of Retention Discourage Its Use In Practice Purely Age-Based System, By Definition, Performs Social Promotion Proficiency-Based System, By Definition, Has No Social Promotion Lancastrian And/Or Tutor Based System, Has No Social Promotion

For narration please double click here Asora® Stellar Schools As It Is A Tutor Based System, It Has No Social Promotion ASORA is an acronym: A: Asynchronous On-Demand Instruction S: Self-Paced Instructional Format O: Online Web Based Instructional System R: Rigorous Content In Curriculum A: Assessment Linked Curriculum Definition

For narration please double click here ® Asora Advantages The Asora Stellar Schools Are Designed To: Employ Automation Where It Makes Sense Use Star Instructors To Create And Present The Content Stellar Schools Have Three Principal Advantages: Significantly Lower Per-Student Costs Better Instruction, Including Better Teachers And Content Social Promotion Is Ended And Subject Mastery Is Assured

Confidence-Based Learning Assessment & Instruction From Knowledge Factor TM Student’s State Of Knowledge: Ignorance: Does Not Know The Concept Or Fact Partial Knowledge: Can Recognize Some Wrong Answers Competence: Knows The Concept Or Fact Misconception: Falsely Believes An Untrue Concept Or Fact For narration please double click here

Double Click in Picture for Video Presentation Physics with Calculus by David V. Anderson Peter Tarsi June 10, 2008 Lecturette 1: Preliminaries Welcome to Asora’s Stellar Schools course Physics with Calculus. This is the first of several hundred short lectures that cover the course. We call these short presentations “lecturettes. ” My name is David Anderson and I am one of two instructors for this course. Peter Tarsi, here on my right, is the other. Mr. Tarsi will now give you a little background information about this course specifically and about the Stellar Schools instructional format in general.

Double Click in Picture for Video Presentation Not Following Hillsdale This Time Thank you Mr. Anderson. Before we dive into the physics course material, I want to tell you about our methods of instruction- especially for newcomers to Stellar Schools who may not have been in a course structured like this before. As you’re probably aware, most Stellar Schools courses are patterned on the curriculum used by the Hillsdale Academy of Hillsdale, Michigan. This course is an exception to that rule because it uses calculus while the Hillsdale course does not. The Physics Curriculum Our curriculum for Physics with Calculus is taken mainly from the textbooks by Giancoli: Physics for Scientists & Engineers, Volume I, Third Edition Physics for Scientists & Engineers, Volume II, Third Edition By Douglas C. Giancoli Prentice Hall A few additional curriculum items were taken from Kaplan Publishing’s AP Physics B & C review book to insure that our course meets the AP curricular requirements as well. Now since Mr. Anderson developed the instructional formats for the Physics course, we’ll ask him what this is all about.

Double Click in Picture for Video Presentation Curriculum is the Universe of Examination Questions In this course and others provided by Stellar Schools, we want to have a clear presentation of what is in the curriculum and what is not. We define it operationally and with a great deal of specificity. Accordingly, our definition of the curriculum for this course (as with all Stellar Schools courses) is simply the “universe” of all possible examination questions and answers that pertain to it. Ideally, students would be questioned on the thousands of facts and concepts that typically define a course’s curriculum. Practical considerations limit any given exam to well less than 100 questions and thus any given test will only measure a student’s mastery of a random subset of the course’s knowledge base.

Double Click in Picture for Video Presentation Mastery is a 95% Score Yes, as Mr. Anderson alludes, there is a tradeoff between measuring a student’s comprehensive knowledge, which favors more test questions to the time and expense required to administer each examination, which favors fewer test questions. Since Stellar Schools expects students to demonstrate their mastery by getting examination scores of 95% and above we wanted to choose the number of questions in a consistent fashion in such a way that exactly 95% is one of the scores. As your mathematical knowledge or intuition will suggest, this means the number of questions needs to be an integer multiple of 20. We currently use tests of 60 questions. If you get 3 or fewer wrong, your score will be 95% or higher allowing you to be certified as having mastered the course. Let’s now ask Mr. Anderson to tell you about Learning Concept Statements (LCS) and Learning Concept Numbers (LCN).

Double Click in Picture for Video Presentation Learning Concept Statements I earlier mentioned that the curriculum is the examination database. We organize the examination database by first building a related database of knowledge items. Each such knowledge item is called a “learning concept statement” or LCS. To keep track of each LCS we assign a Learning Concept Number or LCN to facilitate organizing the course’s full set of LCS’s into a database. Additionally, we combine related Learning Concept Statements into a Learning Concept Group or LCG, which would roughly correspond to a section within a textbook chapter. Related to concept of the LCG, is the Lecturette, which is a short lecture format presentation of the content associated with that Learning Concept Group’s set of Learning Concept Statements (LCS). So for example, this lecturette you’re watching here corresponds to LCG = 1. Given that LCG 1 is focused on housekeeping issues you’ll not be surprised to learn that there are only two physics related LCS presented in this first lecturette. Examinations you will take to demonstrate your mastery of this course will be based only on the collection of LCS presented in this course and on those from prerequisite mathematics and science courses. The LCS for each course are maintained in a spreadsheet. Physics Course Learning Environments As with other Stellar Schools courses, in this physics course we provide several overlapping ondemand learning environments to help students master the content. There are twelve such components. Mr. Tarsi, would you elaborate on them?

Double Click in Picture for Video Presentation Twelve Instructional Components Yes, as presently conceived the twelve instructional components are: 1. Lecturettes: For each Learning Concept Group students may, on demand, view/hear short video lectures presented by the instructional team, which in the case of physics has two teachers and two student questioners. By “short” we mean that these lecture segments rarely run longer than 10 minutes. 2. Supplemental Lecturettes: For a subset of Learning Concept Groups, which students often find more difficult than others, we present additional short lectures to help students “around” common mistakes and misconceptions. 1. Lecturette Notes Online: Expanded “scripts” of the Lecturettes are presented online in textbook format and is the primary textbook for the course as it contains all of the Learning Concept Statements and explanatory material that the student is expected to master. Material from the Supplemental Lecturettes is included in its appendices. 2. Lecturette Notes Hardcopy: A physical paper bound version of the Lecturette Notes is also provided to each student. 3. Secondary Text Hardcopy: A physical “trade” textbook. In fact, this course uses the aforementioned calculus based textbooks by Giancoli. 6. Secondary Text Online: When available, an e-book version of the secondary textbooks will be provided as well. Giancoli’s book is not available in this format.

Twelve Instructional Components Cont. Double Click in Picture for Video Presentation 7. Confidence Based Assessment System: We use the assessment system of Knowledge. Factor, which we describe in more detail in a following section. By knowing the confidence with which a student may hold a misconception, it enables the instructional systems to better remediate the misunderstanding. Practice tests and official tests are drawn, in each instance, from a random sampling of the examination data base- the only difference being that official tests are proctored. 8. Cyber. Tutor: After each test administration, the Cyber. Tutor compiles a remediation document that includes textual and video presentations of the issues and concepts surrounding each question answered incorrectly. This means that you’ll encounter your video instructors again in this mode. 9. Cyber. Games: Various computer games will be organized around the concepts of this course. Each will be designed such that students who have mastered the physics course will tend to win more often. 10. Schoolroom Teacher: Within each Stellar Schools schoolroom there will be at least one teacher- operating in tutoring mode- who can help you learn the material. 11. Student Tutors: Many schoolrooms will also use advanced students as student tutors. To be accorded the status of student tutor, the student must have mastered the relevant courses at a higher level. 12. Hub Help Desk: Finally, at the Stellar Schools Central Service Center or Hub- from which we operate the Stellar Schools network- additional teachers will be available to answer questions when the resources at the schoolroom level prove inadequate.

Double Click in Picture for Video Presentation Bob Asks If This Long List is Superflous? Thanks, Mr. Tarsi. I see we have a hand raised. Yes, Bob, go ahead. Bob asks, “Gee, I’m a little confused about all these different methods of learning the course materials. Are all of these twelve things really necessary? Won’t it take a lot of time to study if we have so many different ways to study the course? ” Mr. Anderson responds: That’s a good question, Bob. It leads into the next comment I was going to make anyway.

Double Click in Picture for Video Presentation Many Options Provide Flexibility While this list of services may seem overwhelming, we don’t require students to use any of them except # 7 - the assessment service. It’s for the student and his or her tutors to decide how best to use these services in their efforts to master the course content. Rather than being ominous, the wide variety of services give you choices from which you can choose what approaches are most comfortable or suitable for your learning styles. And if you enjoy games, you’ll learn that way too. As to the time you’ll devote to studying the concepts in this course, we find that certain difficult concepts, which can differ from student to student, are what often “stump” a pupil. That often leads to much time being spent in an effort to resolve the confusion. With the many different approaches used in this course, we think students will be able to use more than one of them or even several to finally understand a concept that had previously bedeviled them. That can actually be a time saver when confusion is more quickly overcome. And I should add, we provide convenient crossindexing so you can quickly find the pertinent areas within each component. So I’d say that I think this variety provides you with a rich learning environment in which to pursue this fascinating body of knowledge. About The Physics Curriculum Database As we have said, all of the Learning Concept Statements (LCS) are maintained in a database, which serves to operationally define the course curriculum. An associated database containing the actual universe of examination questions more precisely defines the course curriculum.

Double Click in Picture for Video Presentation Learning Concept Statement Example For an example of how this database is organized, we show the LCS corresponding to the course’s Learning Concept Number (LCN) 579 in the figure shown below. The graphic shown here displays one of the Learning Concept Statements (LCS), that for Learning Concept Number (LCN) 579 as it appears in the spreadsheet that is used to define the course curriculum. The lecture notes also display these same graphic representations for all of the course’s LCS’s. It also provides the relevant textbook chapter number together with the LCN. They enable you to find relevant information in the various course materials- both hardcopy and online. The remaining four columns show the concept name, its description, an idealized question, and the answer to that question.

How Examinations Derive From Learning Concept Statements Double Click in Picture for Video Presentation In the preceding display a possible question and its correct answer were shown in the last two columns. In practice there will be many different “sub-species” questions and answers pertaining to each LCS (Learning Concept Statement). The course is designed so you will be able to answer any of these questions if you understand the LCS (and all previous LCS because in most cases a concept builds on items learned earlier). Thus the banks of examination questions will contain far more questions than the number of LCS on which they are based because as we have just indicated there will often be several questions for each LCS. It is for convenience in record keeping- both the school’s and the student’s- that each learning concept (knowledge item) has been assigned a Learning Concept Number (LCN). I see Ann has her hand up. Go ahead Ann.

Can a Question Cover More Than One LCS? Double Click in Picture for Video Presentation Ann asks, “Does this mean that there would be questions that test more than one Learning Concept Statement? ” Yes, that’s right. In fact, many questions will be of that form because it will allow a 60 question test to cover many more than 60 LCS (Learning Concept Statements). “Should I then get a question wrong, how will I find the various portions of text and other materials relevant to the LCS’s that were tested? ” Well, each question will be tagged with a primary LCN number and possibly one or more secondary LCN numbers. That will allow you to rapidly find the content areas tested by the question. An example of this linking will be shown shortly.

Nothing Else is Tested Except the Learning Concept Statements Double Click in Picture for Video Presentation What this all means is that examinations you will take to demonstrate your mastery of this course will be based only on the collection of “learning concept statements” (LCS) presented in this course and on those from prerequisite mathematics and science courses. There are well over two thousand LCS in Physics with Calculus but any examination, for practical reasons discussed earlier, will only employ a small subset of questions addressing the subject matter. That subset will be determined by applying a random number generator to each subtopic in this course. Thus, if and when you retake the course’s examination, the questions will almost always be different than those encountered before- though they will be covering similar or related “ground. ”

Example of LCN 579’s Two Questions Double Click in Picture for Video Presentation Corresponding to LCN 579, just shown, a number of different examination questions could be posed. Two such possible questions, as they would appear in the examination instructions, are shown in the next section. Our examinations apply the most advanced assessment methodologies of which we are aware. We have been working with Knowledge. Factor, Inc to develop a confidence based examination system in which students are assessed according to the two parameters of competence and confidence. We want to know how students arrive at wrong answers. Do they simply guess? Or do they “confidently” know something that “just ain’t so”- quoting here from Mark Twain who had some thoughts in this area. As you will see from the choices presented to the students, the examinations will gauge both of these important parameters. In turn, subsequent remedial efforts will be more effective if we have a better understanding about a student’s confident knowledge.

Double Click in Picture for Video Presentation Example Question #1 Some examples will help. Let me show you two of the examination questions that pertain to LCN 579. As the nearby display shows, a nominal four-prong multiple choice question opens up to provide the student many other choices (14 in all) to demonstrate partial mastery of the concept. As is evident the top four choices are simply those of a standard multiple-choice format. The remaining choices allow you to indicate various “states” of lower confidence. Another question pertaining to LCN 579 is shown next.

Double Click in Picture for Video Presentation Example Question #2 This example question depends on two LCN: 579 and 576. If each question, say, depended on two LCS’s then a 60 question examination, could, in principle, test on 120 concepts.

Double Click in Picture for Video Presentation On Partial Knowledge When students do not confidently know one of the first four answers, they should choose one of the other combination answers. Accordingly, students who choose items with “dual uncertainty” (e. through j. ) are in what might be called a “sort of know” status. Others who choose among the “triplet” items (k. through m. ) have what we’ll call a “whiff” of knowledge because they can identify only one alternative as being false. Finally, those with no knowledge of the answer would choose item n.

Perspective on the Confidence Based Assessment System Double Click in Picture for Video Presentation One way to look at the confidence based assessment system is that it gives the teaching staff and the student a better indication of where they are ignorant, where they have misconceptions, and where they are truly knowledgeable. With this better information, these parties can then better apply remedial measures. In the case of ignorance, the solution is, if you will, education. But in the case of misconceptions, a more intensive process of re-education is advised.

Double Click in Picture for Video Presentation What is Physics? Before concluding Lecturette 1, we wanted to provide an extremely brief introduction to the subject of physics. What is it? It is simply (or complicatedly if you like) the study of the four fundamental forces found in nature. Sometimes physicists talk about the four fundamental interactions instead of forces, but their names remain the same: gravity, electromagnetism, strong nuclear, and weak nuclear. Our first Learning Concept Statement (LCS) for LCN = 1 recites this list.

Physics Relationship to other Sciences Double Click in Picture for Video Presentation These four interactions or forces underlie the mechanisms of all other sciences. Chemistry, for example, is built on a foundation of physics. The two of them together, in turn, form the basis of several other sciences including, biology, geology, astronomy, and a host of other disciplines dependent on combinations of these. Sometimes it is said that mathematics is even more basic than physics and as a subject that is true. However, mathematics is not a science in the sense that science studies phenomena of the real world and universe. Rather, mathematics is a logical structure and quantitative language upon which physics and other sciences are described and evaluated. Given this relationship of physics to the other sciences, brings us to LCN 2 which states that physics is the most basic science.

Lecturette Summary: Double Click in Picture for Video Presentation Physics With Calculus Course Preliminaries As in other courses in the Stellar Schools core curricula, Physics with Calculus is taught through a variety of approaches, with twelve different modes of learning applied. The curriculum is essentially defined by the examination database and its many Learning Concept Statements (LCS). You are expected to achieve a mastery level of competence in the examinations by attaining scores of 95% or higher. Our assessment system measures both the content mastery of each student and his or her confidence level in that mastery. It is unlikely that you will master the course in your first attempt at taking the examination, but after further review you will find your scores increasing until you surpass the 95% level at which point you’ll receive certification that you mastered Physics with Calculus.

Double Click in Picture for Video Presentation Preview of Lecturette 2: The Scientific Method & the Nature of Science is more than a field of study. It is also a method of study. Physics is both a field of study and it depends on a method of study, which we call the “Scientific Method. ” Thus physics is a science. The conjectures, ideas, and theories of physics are explanations of physical phenomena. Only those that can be proven through repeated observation and experiment become the accepted scientific theories of physics. The description of physical phenomena is often quantified by means of mathematics. The mathematical discipline of calculus was originally developed for physics applications.

Double Click in Picture for Video Presentation Physics with Calculus by David V. Anderson & Peter Tarsi assisted by students Carolyn Mc. Crosson & Andrew Trott Lecturette 149: The Maxwellian Speed Distribution In the previous lesson we discussed the concept of a particle distribution function . If tells you, according to the speed or velocity of particles how many particles have any particular speed. Next we explore a special distribution function, which in many cases is both a good physical approximation and is easily manipulated algebraically.

Double Click in Picture for Video Presentation Model of James Clerk Maxwell Lecturette 149 presents information about the Maxwellian Speed Distribution. Well known 19 th century physicist James Clerk Maxwell, using concepts from the field of statistical mechanics, derived a formula for the speed distribution, , of particles (molecules or atoms) likely to be encountered when the particles randomly collide with one another. is the number of particles per unit interval of . While the derivation of this distribution is beyond this course’s scope, the resulting Maxwellian Distribution is given in LCN 584 as shown below:

What is Statistical Mechanics? Double Click in Picture for Video Presentation Ann asks, “What on earth is statistical mechanics- I’ve never heard of it? ” Surely you remember our lessons on the kinematics and dynamics of one and two particle systems? The basic model for statistical mechanics is simply the combination, or overlay, or superposition of a vast number of such single particle systems all made to occupy the same volume. It also assumes two-body collisions or interactions. Now statistical mechanics, as a formal physics course, in generally taught in graduate school or in upper-level undergraduate courses. I might add that the ideal gas law and the zeroth law of thermodynamics, which we recently covered, can also be derived from statistical mechanics. Does this answer your question? “ So I infer from what you are saying that I must take this Maxwellian formula on faith and perhaps wait years until I take a statistical mechanics course where I’ll finally understand where this distribution originated? ” I’m afraid that’s right. Nevertheless, the Maxwellian distribution is also seen experimentally- giving us further assurance that it is correct and giving us more reason to study it now.

Double Click in Picture for Video Presentation Variables and Parameters of Maxwellian

Double Click in Picture for Video Presentation Partial Integration Methods for the Maxwellian As we learned earlier in LCN 577 and LCN 581, the zeroth and first moments of a particle speed distribution function equal the particle number, N , and the average speed, , respectively. Calculating the moments of LCN 584 requires a high level of competence in integral calculus. Our interest here is the zeroth moment and the first moment of the Maxwellian speed distribution. Given the foregoing definition of as a particle number distribution function, it should be evident that the zeroth moment of this distribution will generate the number of particles within the volume of study, which in this case is the norm (which by definition is always the zeroth moment). Its first moment produces the average speed of those particles.

Double Click in Picture for Video Presentation Bob Asks How Zeroth Moment Produces N Bob asks, “I don’t get it. How is this zeroth moment- this integral over the Maxwellian going to produce the number of particles? ” I can answer it two ways. First, the particle number N is part of the coefficient in the Maxwellian formula and thus once the integration is carried out the result will be proportional to N- this is something that is clear from the mathematics of it.

Partial Integration Result for Zeroth Moment of Maxwellian Double Click in Picture for Video Presentation Getting back to the zeroth moment, it is clear from the form of the Maxwellian formula in LCN 584 that evaluating the zeroth moment will require evaluating an integral of the form shown below in LCN 585. Students are not expected to demonstrate their ability to derive the result shown in LCN 585 using integration by parts and the “squares” reduction. For those who are interested in its derivation we’ll discuss the methods employed in a moment. Even for students who know how to derive LCN 585, you are nevertheless advised to memorize it given the significant time required to go through the derivation each time an evaluation is needed.

Integration by “Tricks” We say “integration by tricks” not to imply the use of an improper technique, but we say it to suggest the method is quite unusual and not at all obvious. Double Click in Picture for Video Presentation

Double Click in Picture for Video Presentation Partial Integration for First Moment The other integral, required to evaluate the average speed of the Maxwellian distribution, is based on the partial integration relationship shown below in LCN 586.

Double Click in Picture for Video Presentation Norm or Zeroth Moment of Maxwellian Using LCN 585 to evaluate the zeroth moment of LCN 584 one obtains the relation shown below in LCN 587. By definition this integral over any particle distribution function results in the number of particles, N. A good homework exercise is to use LCN’s 584 and 585 to prove this relation. Next we consider the first moment of a particle speed distribution function. It is of course, the average speed of those particles.

Double Click in Picture for Video Presentation What about Velocity Distributions? Ann asks, “You keep referring to speed. Is this also true for velocity distributions? ” Generally, a velocity distribution is different as it is a vector quantity- unlike speed, which is a scalar. Yet, in the specific case of the Maxwellian the speed always enters as a square meaning that the velocity squared, which equals the speed squared, can be used as well. We recommend that you not confuse yourselves by thinking of these as velocity distributions as there are other particle distributions functions, that you may encounter later, for which the vector nature of the distribution will be important and where the concept of a speed distribution may not be well defined. I hope this answers your question.

Evaluating the Maxwellian First Moment Double Click in Picture for Video Presentation Let’s see, where we? We were about to use LCN 586 to evaluate the Maxwellian distribution’s first moment. Doing that results in the following formula shown below in LCN 588. Students often look at this integral and don’t at first see how it produces an average speed. If you remember that an integral is a special sum and that this particular sum is adding speeds that are multiplied by the percentage of particles at each speed ( divided by N) you will realize that it is an average.

Double Click in Picture for Video Presentation Most Probable Speed of Maxwellian In the next Lecturette (# 150) we will compare three characteristic speeds, the root- mean-square, the average, and the most probable, of the Maxwellian distribution of speeds.

Double Click in Picture for Video Presentation Lecturette Summary: The Maxwellian Speed Distribution In studying the motions of a large number of point particles (or monatomic molecules), usually in instances where the particles collide among themselves, their speeds or velocities are found to be distributed according to the Maxwellian formula. The numbers of particles and their average speed are given by the zeroth and first moments of the Maxwellian distribution, which we have shown can be evaluated in closed form. Another characteristic of the Maxwellian distribution is the most probable speed, which is also given in a closed formula. Many experiments also validate this distribution of speeds. Thus the Maxwellian is not only a good physical approximation, it is relatively easy to use in evaluating macroscopic properties associated with it- such as particle numbers and their average speeds.

Preview of Lecturette 150: Characteristic Speeds of Maxwellian & PV Diagrams Double Click in Picture for Video Presentation We finish the discussion on Maxwellian speed distributions by evaluating the three characteristic speed formulas. Then, in terms of the PV diagram we discuss the regions and limits in which the ideal gas law is valid and develop a descriptive nomenclature including the concept of the critical point.