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# Pressure, temperature and ‘rms’ related to kinetic model

The macroscopic properties of a gas, pressure and temperature, are explained in terms of molecule movement of the Kinetic Theory. The derivation of formulas are shown in logical steps for pressure, temperature and KE.
Published on: Mar 4, 2016

#### Transcripts - Pressure, temperature and ‘rms’ related to kinetic model

• 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 /Russian p=pressure n=molecular density m0=mass of a molecule <v>2= average velocity IB, SAT and Giancoli P=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 = Δmvx = mvx-(-mvx) =2mvx Δt Δt 2L/vx F = mvx2 P = F = mvx2 /L L A L2 P= mvx2 = mvx2 This Pressure for L3 V for one molecule 2L= vxΔt → Δt = 2L/vx
• 6. The Pressure for N molecules and ‘mean square velocity’ • N molecules move at an average velocity = N • Velocity is a vector so In Russian/Kazakh ‘n’ = N/V and is called molecular density. So the Course Plan Formula is and • So P = 1 Nm 3V ‘n’ = 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. vrms 3RT M Because:
• 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 M 3 8.31J mol K 293 K 0.0280 kg mol 511 m s 3 8.31J mol K 293 K 0.0320 kg mol 478 m s For oxygen… vrms 3RT 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 • Therefore and
• 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