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Major Concepts in Physics Lecture 14.

Major Concepts in Physics Lecture 14. . Prof Simon Catterall Office 309 Physics, x 5978 smc@physics.syr.edu http://physics/courses/PHY102.08Spring. Plan for today … quick tour of some concepts of thermodynamics …. Temperature, heat. Thermal equilibrium Ideal gases – gas laws

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Major Concepts in Physics Lecture 14.

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  1. Major Concepts in Physics Lecture 14. Prof Simon Catterall Office 309 Physics, x 5978 smc@physics.syr.edu http://physics/courses/PHY102.08Spring PHY102

  2. Plan for today … quick tour of someconcepts of thermodynamics … • Temperature, heat. Thermal equilibrium • Ideal gases – gas laws • Real gases – molecular interactions • Internal energy, work and 1st law of thermodynamics PHY102

  3. Temperature • This is a measure of the mean kinetic energy of the atoms/molecules that comprise body • Simplest ex. Ideal gas. Gas comprises a (very) large number of atoms in random motion • I mole=number atoms in 12 g of carbon Assume all atoms move independently except for collisions PHY102

  4. Absolute (Kelvin) temperature • Mean kinetic energy=1/2m<v2> = 3/2 kT <v2> means average squared speed Same temperature scale we used for thermal radiation Square root of this is called the rms speed k = 1.3810-23 J/K is Boltzmann’s constant PHY102

  5. The distribution of speeds in a gas is given by the Maxwell-Boltzmann Distribution. PHY102

  6. Example (text problem 13.70): What are the rms speeds of helium atoms, and nitrogen, hydrogen, and oxygen molecules at 25 C? On the Kelvin scale T = 25 C = 298 K. PHY102

  7. Thermal equilibrium BB A A A B A A A AAAA Molecules mix andeventually attain same Mean kinetic energy – same temperature A Molecules mix and eventually attain same Mean kinetic energy – same temperature! A A A A A A A A f f h PHY102

  8. Gas demo - Heat • Independent of size of ‘’atoms’’ and their initial motion they all end up carrying same energy after many collisions • We often say that when two objects are placed in thermal contact heat flows between them until their temperatures are equalHeat is thus energy in transit PHY102

  9. Fig. 14.9a PHY102

  10. Pressure of ideal gas • The pressure of a gas is a measure of the mean force per unit area exerted by the atoms of the gas on the walls of its container • Arises as atom changes direction after colliding with wall change of momentum • Depends on how many atoms are in container and speed with which they move PHY102

  11. . PHY102

  12. Ideal gas law • Find P=2/3 N/V x (mean kinetic energy K) • Using K=3/2 kT  P=(Nk)/V T=n(NAk)/V T or PV=nRT where gas constant R=NAk=8.31 J/mole n number of moles present PHY102

  13. Gas demos • Pressure varies linearly with temperature PHY102

  14. Fig. 13.10c PHY102

  15. Internal energy U • The internal energy of a gas/body is the sum of all molecular energies • For an ideal gas: just kinetic energy • For real gas: • Potential energy associated with intermolecular forces (electrical in origin) • Energy of vibration and rotation for molecules PHY102

  16. An ideal gas is compressed so that its volume halves while keeping its temperature constant. Does its internal energy … • Increase • Decrease • Stay the same • Need more info … PHY102

  17. Heating • When heat Q is applied to body we will increase its internal energy U • Usually some of this internal energy is kinetic and hence its temperature T increases T1T2 • Typically: Q=mC(T2-T1) m= mass, C = specific heat capacity. Depends on substance .. PHY102

  18. Example (text problem 14.12): If 125.6 kJ of heat are supplied to 5.00102 g of water at 22 C, what is the final temperature of the water? PHY102

  19. Work • There are two ways to increase internal energy of body – either by adding heat Q OR • Doing work on the body eg compressing it • Imagine molecules connected by little springs. Compress the system a little – this takes mechanical work (PHY101). It increases the stored energies in these molecular springs. After the springs relax will also increase molecular kinetic energy. PHY102

  20. Work on a gas • Work done compressing a gas at constant pressure from V1 to V2 is just P(V1-V2) • Think of gas in cylinder contained by piston V=Ax. W=Fx=(F/A) Ax=P(V1-V2) x V2 V1 PHY102

  21. 1st law of thermodynamics • Generalizes conservation of (mechanical+electrical) energy learnt in PHY101 to all types of energy • Specifically including heat Q and internal energy U. • Write DU=Q+W PHY102

  22. Fig. 14.3 PHY102

  23. Demo • Electrical power=current x voltsconverted to heat • Heat transferred to water  raises its internal energy U • Leads to change in temperature • Calculate amount of electrical heat applied. • Calculate heating of liquid from specific heat capacity  Find they are equal Conservation of energy!! PHY102

  24. Summary • Temperature as kinetic energy of molecular constituents. • Ideal gas model: atoms in rapid, random motion  molecular description of pressure, Ideal gas equation • Internal energy: kinetic plus internal potential energy (real gases ….) • Change U thru heat Q and/or work W • 1st law of thermodynamics – energy is conserved! PHY102

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