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Lecture 28: Wrap-up of Chapter 19 and Introduction to Waves (EN)

This lecture covers the concepts of heat engines and refrigerators from Chapter 19, and introduces the topic of waves from Chapter 20. It includes a reading assignment for the next class and a reminder about the upcoming homework deadline.

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Lecture 28: Wrap-up of Chapter 19 and Introduction to Waves (EN)

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  1. Lecture 28 Goals: • Wrap-up chapter 19, heat engines and refrigerators • Start discussing Chapter 20, Waves • Reading assignment for Monday: Chapter 21.1, 21.2. • HW 11 due Wednesday, Dec 15

  2. Turbines: Brayton Cycle Wout=QH-QC

  3. Which of the following processes would have the largest work output per cycle? A) B) C) P P P V V V

  4. Internal combustion engine: gasoline engine • A gasoline engine utilizes the Otto cycle, in which fuel and air are mixed before entering the combustion chamber and are then ignited by a spark plug. Otto Cycle (Adiabats)

  5. The best thermal engine ever, the Carnot engine • A perfectly reversible engine (a Carnot engine) can be operated either as a heat engine or a refrigerator between the same two energy reservoirs, by reversing the cycle and with no other changes.

  6. The Carnot Engine • Carnot showed that the thermal efficiency of a Carnot engine is: • All real engines are less efficient than the Carnot engine because they operate irreversibly due to the path and friction as they complete a cycle in a brief time period.

  7. For which reservoir temperatures would you expect to construct a more efficient engine? A) Tcold=10o C, Thot=20o C B) Tcold=10o C, Thot=800o C C) Tcold=750o C, Thot=800o C

  8. Chapter 20, Waves • A traveling wave is a disturbance propagating at a well-defined wave speed v. • In transverse waves the particles of the medium move perpendicularto the direction of wave propagation. • In longitudinal waves the particles of the medium move parallelto the direction of wave propagation.

  9. t=0 A wave is a propagation of disturbance and transfers energy, but no material or substance is transferred. t=1s Displacement, D t=2s x

  10. Types of Waves • Mechanical waves travel through a material medium such as water or air. • Electromagnetic waves require no material medium and can travel through vacuum. Examples: • Sound waves (air moves locally back & forth) • Water waves (water moves up & down) • Light waves(an oscillating electromagnetic field)

  11. Speed of Waves Δx Δt v=Δx/Δt

  12. The displacement function For a one dimensional wave (one spatial dimension), the displacement is a two dimensional function. t=0 D(x,t=0) t=1s Displacement, D D(x,t=1) t=2s D(x,t=2) x D(x,t): displacement at position x, at time t

  13. Sinusoidal waves • “Continuous waves” that extend forever in each direction ! D(x,t=0) v x A A: Amplitude of the wave

  14. Sinusoidal waves • The displacement is sinusoidal in time at some fixed point in space. D(x=0,t) t A

  15. D(x=0,t) t T: period T D(x,t=0) x λ: wavelength λ

  16. Relationship between wavelength an period v D(x,t=0) x x0 λ T=λ/v

  17. Exercise • The speed of sound in air is a bit over 300 m/s (i.e., 343 m/s), and the speed of light in air is about 300,000,000 m/s. • Suppose we make a sound wave and a light wave that both have a wavelength of 3 meters. What is the ratio of the period of the light wave to that of the sound wave ? (A) About 1,000,000 (B) About 0.000.001 (C) About 1000

  18. Mathematical formalism D(x=0,t) D(0,t) ~ A cos (wt + f) • w: angular frequency • w=2π/T t T λ D(x,t=0) D(x,0) ~ A cos (kx+ f) • k: wave number • k=2π/λ t

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