Physics 207: Lecture 28, Pg 1

Lecture 28Goals:Goals:

• Wrap-up chapter 19, heat engines and refrigeratorsWrap-up chapter 19, heat engines and refrigerators

• Start discussing Chapter 20, WavesStart discussing Chapter 20, Waves

• Reading assignment for Monday: Chapter 21.1, 21.2.

• HW 11 due Wednesday, Dec 15

Physics 207: Lecture 28, Pg 2

Turbines: Brayton Cycle

Wout=QH-QC

Physics 207: Lecture 28, Pg 3

Which of the following processes would have the largest work output per cycle?

V

P

V V

P PA) B) C)

Physics 207: Lecture 28, Pg 4

Internal combustion engine: gasoline engine

(Adiabats)

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 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

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.

Carnot showed that the Carnot showed that the thermal efficiency of a thermal efficiency of a Carnot engine is:Carnot engine is:

hot

coldcycleCarnot T

T1

Physics 207: Lecture 28, Pg 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

Physics 207: Lecture 28, Pg 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 perpendicular to the direction of wave propagation.

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

Dis

plac

emen

t, D

Physics 207: Lecture 28, Pg 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)

Physics 207: Lecture 28, Pg 11

Speed of Waves

Δt

Δx

v=Δx/Δt

Physics 207: Lecture 28, Pg 12

The displacement functionFor a one dimensional wave (one spatial dimension), the displacement is a two dimensional function.

t=0

t=1s

t=2s

x

Dis

plac

emen

t, 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

“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

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

x0

T=λ/v

Physics 207: Lecture 28, Pg 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

Physics 207: Lecture 28, Pg 18

Mathematical formalismD(x=0,t)

t

T

D(0,t) ~ A cos (t + ) angular frequency

π

D(x,t=0)

t

λ

D(x,0) ~ A cos (kx+ )k wave number

k=2π/λ