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NATS 101

Lecture 4

Radiation

What is Temperature?

Microscopic View

Energy due to random jiggling of molecules

Related to average molecular speed; 500 m/s (=1100 mph) at room temperature for air

Modes of Heat Transfer

Williams, p. 19

Latent Heat

Take Home Concepts

• Heat-Energy transfer due to temperature differences

Four modes of heat transfer

Conduction – molecule to molecule

Convection – transport of fluid

Radiation – electromagnetic waves Latent Heat – energy of phase changes

Radiation

• Any object that has a temperature greater than 0 K, emits radiation.

• This radiation is in the form of electromagnetic waves, produced by the acceleration of electric charges.

• These waves don’t need matter in order to propagate; they move at the “speed of light” (3x105 km/sec) in a vacuum.

Electromagnetic Waves

• Two important aspects of waves are:– What kind: Wavelength or distance between

peaks.– How much: Amplitude or distance between peaks

and valleys.

Wavelength

Amplitude Frequency

Why Electromagnetic Waves?

• Radiation has an Electric Field Component and a Magnetic Field Component– Electric Field is Perpendicular to Magnetic Field

Photons

• NOT TO CONFUSE YOU, but…

• Can also think of radiation as individual packets of energy or PHOTONS.

• In simplistic terms, radiation with – shorter wavelengths corresponds to

photons with more energy and – higher wave amplitude to more BB’s per

second

Electromagnetic Spectrum

WAVELENGTH

Danielson, Fig. 3.18

Wavelengths of Meteorology Significance

Emitted Spectrum

White Light from Flash Light

Purple GreenRed

•Emitted radiation has many wavelengths.

Prism

(Danielson, Fig. 3.14)

Emitted SpectrumEnergy from Sun is spread unevenly over all wavelengths.

Wavelength

En

erg

y E

mit

ted

Emission spectrum of Sun

Ahrens, Fig. 2.7

Wien’s Law

The hotter the object, the shorter the brightest wavelength.

Danielson, Fig. 3.19

Wien’s Law

Relates the wavelength of maximum emission to the temperature of mass

MAX= (0.29104 m K) T-1

Warmer Objects => Shorter Wavelengths• Sun-visible light

MAX= (0.29104 m K)(5800 K)-1 0.5 m• Earth-infrared radiation

MAX= (0.29104 m K)(290 K)-1 10 m

Wien’s Law

What is the radiative temperature of an incandescent bulb whose wavelength of maximum emission is near 1.0 m ?

• Apply Wien’s Law:

MAX= (0.29104 m K) T-1

• Temperature of glowing tungsten filament

T= (0.29104 m K)(MAX)-1

T= (0.29104 m K)(1.0 m)-1 2900K

Stefan-Boltzmann’s (SB) Law

• The hotter the object, the more radiation emitted.

• When the temperature is doubled, the emitted energy increases by a factor of 16!

• Stefan-Boltzmann’s LawE= (5.6710-8 Wm-2K-4 )T4

E=2222=16

4 times

Sun Temp: 6000K

Earth Temp: 300K

Aguado, Fig. 2-7

How Much More Energy is Emitted by the Sun per m2 Than the Earth?• Apply Stefan-Boltzman Law

• The Sun Emits 160,000 Times More Energy per m2 than the Earth,

• Plus Its Area is Mucho Bigger (by a factor of 10,000)!

-2 -2 -4

-2

-2

48

8 4

48

4 544

(W m ) W m K

W mW m

(5.67 10 )

(5.67 10 ) (5800 )5.67 ( )( 10 ) 290

(5800 ) 1.6 1020(290 )

Sun

Earth

E T

E KKE

KK

−

−

−

= ×

×=×

= = ×=

Radiative Equilibrium

• Radiation absorbed by an object increases the energy of the object.– Increased energy causes temperature to

increase (warming).

• Radiation emitted by an object decreases the energy of the object.– Decreased energy causes temperature to

decrease (cooling).

Radiative Equilibrium (cont.)

• When the energy absorbed equals energy emitted, this is called Radiative Equilibrium.

• The corresponding temperature is the Radiative Equilibrium Temperature.

Key Points

• Radiation is emitted from all objects that have temperatures warmer than absolute zero (0 K).

• Wien’s Law: wavelength of maximum emissionMAX= (0.29104 m K) T-1

• Stefan-Boltzmann Law: total energy emissionE= (5.6710-8 W/m2 ) T4

Key Points

• Radiative equilibrium and temperatureEnergy In = Energy Out (Eq. Temp.)

• Three modes of heat transfer due to temperature differences. Conduction: molecule-to-moleculeConvection: fluid motionRadiation: electromagnetic waves

Reading Assignment

• Ahrens

Pages 30-42

Problems 2.7, 2.9, 2.10, 2.11, 2.12