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Lecture 28

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. Turbines: Brayton Cycle. W out =Q H -Q C.

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Lecture 28

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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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