1Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterRed Sox - Yankees. Baseball can not getmore exciting than these games.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121, April 17, 2008.Kinetic theory of gases.http://eml.ou.edu/Physics/module/thermal/ketcher/Idg4.aviFrank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.April 17, 2008.• Course Information• Topics to be discussed today:• The ideal gas law (review).• Molecular interpretation of temperature.• The real equation of state.• Quiz2Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.April 17, 2008.• Homework set # 9 is due on Saturday morning, April 19, at8.30 am.• Midterm Exam # 3 will take place on Tuesday April 22between 8.00 am and 9.30 am. The material to be coveredis the material contained in Chapters 10, 11, 12, and 14.• I will distribute the formula sheet that will be attached to theexam later this week via email.• I will review the material covered on the exam on Sundayevening. Further details will be announced via email.• Extra office hours will be offered by the TAs on Sunday andMonday. The schedule will be announced via email.• There will be no class after the exam on Tuesday.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.April 17, 2008.• Workshops schedule next week:• There will be workshops on Monday to answer questions related toExam # 3.• There will be workshops on Thursday and Friday to discuss thesolutions of Exam # 3 and return your blue booklets.• During the week of April 28 there will only be workshops onMonday, Tuesday, and Wednesday.• To increase the efficiency with which we can return the bluebooklets of Exam # 3, you will need to write your workshopday/time on the front of each booklet.• The results of Exam # 3 will be emailed to you on MondayApril 28Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.April 17, 2008.• Grades: Worst case scenario:• Let’s assume you got 0% on exam 1 and 0% on exams 2.• Clearly you would benefit if we drop one of these grades!• If we drop one of these grades, than the one we count will count for20% of your final grade.• If you get 100% on exam # 3 and 100% on the final (and assumingyou have 100% on the homework sets, quizzes, and labs) you end upwith a final grade for 80% or an A!!!!!• No one matches this worst case scenario, but realize that even if youdid poorly on the first two exams, you can still get an A in this course.3Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThe equation of state of a gas.A quick review.• The equation of state of a gas wasinitially obtained on the basis ofobservations.• Boyle’s Law (1627 - 1691):pV = constant for gasesmaintained at constanttemperature.• Charle’s Law (1746 - 1823):V/T = constant for gasesmaintained at constant pressure.• Gay-Lussac’s Law (1778 - 1850):p/T = constant for gasesmaintained at constant volumeFrank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThe equation of state of a gas.A quick review.• The equation of state of a gas can be written aspV = nRTwhere• p = pressure (in Pa).• V = volume (in m3).• n = number of moles of gas (1 mole = 6.02 x 1023 molecules oratoms). Note the number of molecules in a mole is also known asAvogadro’s number NA.• R = the universal gas constant (R = 8.315 J/(mol K).• T = temperature (in K).• Note: the equation of state is the equation of state of an idealgas. Gases at very high pressure and/or close to the freezingpoint show deviations from the ideal gas law.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThe equation of state of a gas.A quick review.• The equation of state of a gas can also be written aspV = nRT = (N/NA)RT = NkTwhere• N = total number of molecules• NA = Avogadro’s number• k = R/ NA is the Boltzmann constant = 1.38 x 10-23 J/K• This is the most frequently used form of the equation ofstate of the gas.4Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThe molecular point of view of a gas.• Consider a gas contained in acontainer.• The molecules in the gas willcontinuously collide with the walls ofthe vessel.• Each time a molecule collides with thewall, it will carry out an elasticcollision.• Since the linear momentum of themolecule is changed, the linearmomentum of the wall will changetoo.• Since force is equal to the change inlinear momentum per unit time, thegas will exert a force on the walls.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThe molecular point of view of a gas.• Consider the collision of a singlemolecule with the left wall.• In this collision, the linearmomentum of the moleculechanges bymvx - (-mvx) = 2mvx• The same molecule will collidewith this wall again after a timeΔt = 2l/vx• The force that this singlemolecule exerts on the left wall isthus equal toΔp/Δt = (2mvx)/(2l/vx) = mvx2/lFrank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThe molecular point of view of a gas.• The force that this singlemolecule exerts on the left wall isthus equal toFleft = mvx2/l• If the pressure exerted on the leftwall by this molecule is equal topleft = Fleft/A = mvx2/(lA)where A is the area of the leftwall.• The volume of the gas is equal tolA and we can thus rewrite thepressure on the left wall:pleft = mvx2/V5Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterThe molecular point of view of a gas.• The pressure that many moleculesexerts on the left wall is equal topleft = m(v1x2+v2x2+v3x2+... )/V• This equation can be rewritten interms of the average of the square ofthe x component of the molecularvelocity and the number of molecules(N):pleft = mN(vx2)average/V• Assuming that there is no preferentialdirection, the average square of the x,y, and z components of the molecularvelocity will be the same:(vx2)average= (vy2)average= (vz2)averageFrank L. H. Wolfs Department of Physics and Astronomy, University