Recall that light is EM Recall that light is EM radiation and is therefore radiation and is therefore characterized by its characterized by its wavelength.wavelength.

Imagine we had the “perfect” Imagine we had the “perfect” emitter of EM radiation. We emitter of EM radiation. We would call that a “Blackbody”. would call that a “Blackbody”.

The Sun (and all stars) give The Sun (and all stars) give off nearly every wavelength off nearly every wavelength of EM radiation.of EM radiation.

But what wavelength But what wavelength dominates?????dominates?????

During this Solar Eclipse (1991) you can see the Corona of the Sun. It is extends hundreds of thousands of Kilometers into

space

The simplest and most The simplest and most common way to produce common way to produce EM radiation is to heat up EM radiation is to heat up an object. an object.

Lets consider the Lets consider the welder here.welder here.

As the temperature As the temperature increases what can we increases what can we say about ...say about ...

The color?The amount of Heat?

blackbody.swf

BLACKBODY CURVES

The Blackbody curve for The Blackbody curve for the Sunthe Sun

When we compare the When we compare the curve for a star to the curve for a star to the curve of a blackbody at curve of a blackbody at a given temp, we can in a given temp, we can in effect...effect...

Take the temperature of a Take the temperature of a star from millions/billions star from millions/billions of miles away!!!of miles away!!!

The equations that The equations that describe these curves are describe these curves are rather complicated. rather complicated.

However, we can deduce However, we can deduce 2 useful expressions. The 2 useful expressions. The first one relates first one relates temperature to wavelength temperature to wavelength of maximum emission.of maximum emission.

aka Wien’s Displacement Law

m ax ( ).

( )m eters

T kelv in

2 9 x 1 0 -3

(PSRT)

Example: Determine Example: Determine the Surface the Surface Temperature of the Temperature of the Sun.Sun.

Assume Assume λλmaxmax is 500 nm is 500 nm

m ax ( ).

( )m eters

T kelv in

2 9 x 1 0 -3

(PSRT)

Thought Experiment. Consider a hot Thought Experiment. Consider a hot metal rod and a burning match at the metal rod and a burning match at the same temp.same temp.

Which gives off more energy???Which gives off more energy???We must consider the amount of energy We must consider the amount of energy

emitted per surface area. emitted per surface area. ENERGY FLUX ENERGY FLUX

The The energy fluxenergy flux is just a fancy way of saying is just a fancy way of saying

“The amount of energy emitted from 1m2 of an object’s surface per second.”

[J/m2/sec] or [W/m2]

So for the match and metal bar, which one has a So for the match and metal bar, which one has a higher energy flux? Neither. But clearly the higher energy flux? Neither. But clearly the match will not do as much damage to your skin. match will not do as much damage to your skin.

So what’s the difference? So what’s the difference?

In 1879, Josef Stefan In 1879, Josef Stefan showed thatshowed that

Five years later Ludwig Five years later Ludwig Boltzmann derived the Boltzmann derived the coefficient that related the coefficient that related the 2 quantities.2 quantities.

Recall Luminosity is the Recall Luminosity is the power output of a star. power output of a star. Therefore....Therefore....

E n erg y F lu x T 4

E n erg y F lu x

w h ere = 5 .6 7 x 1 0 W / m K-8 2 4

T 4L

w h ere

= 5 .6 7 x 1 0 W / m K

L = lu m in o sity

A = c ro ss sec tio n a l a rea

T = tem p in K ek v in

-8 2 4

A T 4

Sample problem: F1 (c) M02 exam

Antares A is part of a binary star system. The companion star Antares B has a surface temperature of 15 000 K and a luminosity that is 1/40 of that of Antares A. Calculate the ratio of the radius of Antares A to Antares B.

Antares A has a surface temperature of 3000 K. This info was provided in an earlier part of the problem (not stated).

In addition, you must know the formula for the surface area of a sphere to solve these types of problems.

24A r

2 42 4

2 4 2 4

18 2 13 2

use Stefan-Boltzmann Law40

(4 )(4 )

40

40 (15000) (3000)

2.025 10 8.1 10

160 (2 SF)

AB

A AB B

B A

B A

A

B

LL

r Tr T

r r

r r

r

r

Worksheet on Worksheet on

Apparent BrightnessApparent BrightnessWien’s LawWien’s LawSB LawSB Law