Red Sox Yankees Baseball can not get more exciting than these games Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 April 17 2008 Kinetic theory of gases http eml ou edu Physics module thermal ketcher Idg4 avi Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 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 Quiz Frank L H Wolfs Department of Physics and Astronomy University of Rochester 1 Physics 121 April 17 2008 Homework set 9 is due on Saturday morning April 19 at 8 30 am Midterm Exam 3 will take place on Tuesday April 22 between 8 00 am and 9 30 am The material to be covered is the material contained in Chapters 10 11 12 and 14 I will distribute the formula sheet that will be attached to the exam later this week via email I will review the material covered on the exam on Sunday evening Further details will be announced via email Extra office hours will be offered by the TAs on Sunday and Monday 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 Rochester Physics 121 April 17 2008 Workshops schedule next week There will be workshops on Monday to answer questions related to Exam 3 There will be workshops on Thursday and Friday to discuss the solutions of Exam 3 and return your blue booklets During the week of April 28 there will only be workshops on Monday Tuesday and Wednesday To increase the efficiency with which we can return the blue booklets of Exam 3 you will need to write your workshop day time on the front of each booklet The results of Exam 3 will be emailed to you on Monday April 28 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 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 for 20 of your final grade If you get 100 on exam 3 and 100 on the final and assuming you have 100 on the homework sets quizzes and labs you end up with a final grade for 80 or an A No one matches this worst case scenario but realize that even if you did poorly on the first two exams you can still get an A in this course Frank L H Wolfs Department of Physics and Astronomy University of Rochester 2 The equation of state of a gas A quick review The equation of state of a gas was initially obtained on the basis of observations Boyle s Law 1627 1691 pV constant for gases maintained at constant temperature Charle s Law 1746 1823 V T constant for gases maintained at constant pressure Gay Lussac s Law 1778 1850 p T constant for gases maintained at constant volume Frank L H Wolfs Department of Physics and Astronomy University of Rochester The equation of state of a gas A quick review The equation of state of a gas can be written as pV nRT where p pressure in Pa V volume in m 3 n number of moles of gas 1 mole 6 02 x 1023 molecules or atoms Note the number of molecules in a mole is also known as Avogadro s number N A 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 ideal gas Gases at very high pressure and or close to the freezing point show deviations from the ideal gas law Frank L H Wolfs Department of Physics and Astronomy University of Rochester The equation of state of a gas A quick review The equation of state of a gas can also be written as pV nRT N NA RT NkT where N total number of molecules NA Avogadro s number k R N A is the Boltzmann constant 1 38 x 10 23 J K This is the most frequently used form of the equation of state of the gas Frank L H Wolfs Department of Physics and Astronomy University of Rochester 3 The molecular point of view of a gas Consider a gas contained in a container The molecules in the gas will continuously collide with the walls of the vessel Each time a molecule collides with the wall it will carry out an elastic collision Since the linear momentum of the molecule is changed the linear momentum of the wall will change too Since force is equal to the change in linear momentum per unit time the gas will exert a force on the walls Frank L H Wolfs Department of Physics and Astronomy University of Rochester The molecular point of view of a gas Consider the collision of a single molecule with the left wall In this collision the linear momentum of the molecule changes by mvx mvx 2mvx The same molecule will collide with this wall again after a time t 2l vx The force that this single molecule exerts on the left wall is thus equal to p t 2mvx 2l vx mvx 2 l Frank L H Wolfs Department of Physics and Astronomy University of Rochester The molecular point of view of a gas The force that this single molecule exerts on the left wall is thus equal to Fleft mvx 2 l If the pressure exerted on the left wall by this molecule is equal to pleft Fleft A mvx 2 lA where A is the area of the left wall The volume of the gas is equal to lA and we can thus rewrite the pressure on the left wall pleft mvx 2 V Frank L H Wolfs Department of Physics and Astronomy University of Rochester 4 The molecular point of view of a gas The pressure that many molecules exerts on the left wall is equal to pleft m v1x2 v 2x2 v3x2 V This equation can be rewritten in terms of the average of the square of the x component of the molecular velocity and the number of molecules N pleft mN vx2 average V Assuming that there is no preferential direction the average square of the x y and z components of the molecular velocity will be the same vx 2 average vy2 average vz 2 average Frank L H Wolfs Department of Physics and Astronomy University of Rochester The molecular point of view of a gas The force on the left wall can be rewritten in terms of the average squared velocity pleft mN v2 average 3V Assuming there is no preferential direction of motion of the molecules the pressure on all walls will be the same and we thus conclude pV mN v2 average 3 Compare this to the ideal gas law …