1. Pressure, Temperature and RMS related to kinetic model Lesson Opener: How does Pressure of a Gas relate to the motion of particles in the Molecular Kinetic Theory?NIS, Taldykorgan Grade 11 Physics

2. Objective 1: Explain how molecular movement causes the pressure exerted by a gas and hence deduce the relationship: Kazakh /Russianp=pressure n=molecular density m0=mass of a molecule 2= average velocityIB, SAT and GiancoliP=pressure N=Number of molecules m=mass of a molecule V=volume =average velocity 3. WHAT CAUSES PRESSURE in a GAS? IF MOLECULES MOVE FASTER AND COLLIDE MORE OFTEN, THEY HAVE MORE FORCE. PRESSURE INCREASES! When you shack a bottle of soda, the gas molecules move faster, pressure increases, when opened the higher pressure explodes with the soda making a big mess. 4. How Does KT explain Pressure? Elastic collisions causes a force on the sides of the container. The force depends on: Mass of molecules Velocity of molecules Number of molecules N=Number of molecules m=mass of a molecule =average velocity 5. Deduce (or Derive) this relationship One molecule creates a force by its change in momentum F= Change in momentum change in time F = mvx = mvx-(-mvx) =2mvx t t 2L/vx F = mvx2 P = F = mvx2 /L L A L2 P= mvx2 = mvx2 This Pressure for L3 V for one molecule2L= vxt t = 2L/vx 6. The Pressure for N molecules and mean square velocity N molecules move at an average velocity = N Velocity is a vector soIn Russian/Kazakh n = N/V and is called molecular density. So the Course Plan Formula isand So P = 1 Nm 3Vn = N V (only here does n= molecular density) 7. YouTube Presentation of Pressure Derivation of Pressure Formula: http://www.youtube.com/watch?v=CmerWVk 0ZaI 8. Root Mean Square Speed Objective 2: Recall and understand the term root mean-square velocity (average = mean) Simply the square root of the average velocity Why? Velocities are + and - , so an average would be zero! Squaring first gives all positive velocities Taking the square give the average speed without direction. Also used in AC current calculations in year 12! 9. Why and Where do we need RMS? To find the velocity of molecules at T! Start with Remember: PV = NkT Therefore: Now, to find velocity we need to take the square root of the average square velocity! 10. Uses of RMS Velocity RMS speed is used to predict how fast molecules are moving at a given Temperature. How fast molecules move is directly proportional to their absolute temperature and inversely proportional to their mass.vrms3RT MBecause: 11. Example: Determine the Speed of Molecules in Air at 293 K? N2 molecules (molecular mass 28.0 u) 3RT O2 molecules (molecular mass 32.0 u) vrms M For nitrogen 3RT vrms M3 8.31J mol K 293 K 0.0280 kg mol511 m s3 8.31J mol K 293 K 0.0320 kg mol478 m sFor oxygenvrms3RT M 12. At the same temperature Small molecules move fast Large molecules move slow 13. Important features of Maxwell-Boltzmann distribution :The speed-density relationship of 4 Gases at 298.15 K (25 C). 14. Kinetic Energy and Temperature: Objective 3: compare and PV=NkT and hence deduce that the average kinetic energy of a molecule is proportional to T ! Remember that Thereforeand 15. References: Learn Physics: Learn about Kinetic Theory of Gases (good animation) http://www.youtube.com/watch?v=YSTRa27a3BQ Pressure and RMS Velocity (Easy Formulas) http://www.youtube.com/watch?v=CmerWVk0ZaI