Physics 207: Lecture 28, Pg 1 Lecture 28Goals: Wrap-up chapter 19, heat engines and refrigerators Wrap-up chapter 19, heat engines and refrigerators Start discussing Chapter 20, Waves Start discussing Chapter 20, Waves Reading assignment for Monday: Chapter 21.1, HW 11 due Wednesday, Dec 15

Physics 207: Lecture 28, Pg 2 Turbines: Brayton Cycle W out =Q H -Q C

Physics 207: Lecture 28, Pg 3 l Which of the following processes would have the largest work output per cycle? V P V V P P A) B)C)

Physics 207: Lecture 28, Pg 4 Internal combustion engine: gasoline engine (Adiabats) l 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

Physics 207: Lecture 28, Pg 5 The best thermal engine ever, the Carnot engine l 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.

Physics 207: Lecture 28, Pg 6 The Carnot Engine l 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. l Carnot showed that the thermal efficiency of a Carnot engine is:

Physics 207: Lecture 28, Pg 7 l For which reservoir temperatures would you expect to construct a more efficient engine? A) T cold =10 o C, T hot =20 o C B) T cold =10 o C, T hot =800 o C C) T cold =750 o C, T hot =800 o C

Physics 207: Lecture 28, Pg 8 Chapter 20, Waves A traveling wave is a disturbance propagating at a well-defined wave speed v. l In transverse waves the particles of the medium move perpendicular to the direction of wave propagation. l In longitudinal waves the particles of the medium move parallel to the direction of wave propagation.

Physics 207: Lecture 28, Pg 9 A wave is a propagation of disturbance and transfers energy, but no material or substance is transferred. t=0 t=1s t=2s x Displacement, D

Physics 207: Lecture 28, Pg 10 Types of Waves l Mechanical waves travel through a material medium such as water or air. l 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)

Physics 207: Lecture 28, Pg 11 Speed of Waves Δt Δx v=Δx/Δt

Physics 207: Lecture 28, Pg 12 The displacement function For a one dimensional wave (one spatial dimension), the displacement is a two dimensional function. t=0 t=1s t=2s x Displacement, D D(x,t=0) D(x,t=1) D(x,t=2) D(x,t): displacement at position x, at time t

Physics 207: Lecture 28, Pg 13 Sinusoidal waves l “Continuous waves” that extend forever in each direction ! A D(x,t=0) x A: Amplitude of the wave v

Physics 207: Lecture 28, Pg 14 Sinusoidal waves l The displacement is sinusoidal in time at some fixed point in space. A D(x=0,t) t

Physics 207: Lecture 28, Pg 15 D(x=0,t) t T D(x,t=0) x λ T: period λ: wavelength

Physics 207: Lecture 28, Pg 16 Relationship between wavelength an period D(x,t=0) x λ v x0x0 T=λ/v

Physics 207: Lecture 28, Pg 17 Exercise l 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. l 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 (C) About 1000

Physics 207: Lecture 28, Pg 18 Mathematical formalism D(x=0,t) t T D(0,t) ~ A cos (  t +  )  angular frequency   D(x,t=0) t λ D(x,0) ~ A cos ( kx +  )  k  wave number  k=2π/λ