PTYS 214 – Spring 2011

Homework #4 DUE in class TODAY

Reminder: Extra Credit Presentations (up to 10pts) Deadline: Thursday, Mar. 3(must have selected a paper)

Class website: http://www.lpl.arizona.edu/undergrad/classes/spring2011/Pierazzo_214/

Useful Reading: class website “Reading Material” http://www.solstation.com/habitable.htm http://en.wikipedia.org/wiki/Greenhouse_effect http://www.lsbu.ac.uk/water/vibrat.html

Announcements

Three major advantages of Water

1. A wide (and high) range of temperatures over which it remains liquid (major advantage)

2. Water ice floats, whereas the other substances sink when frozen (also important)

3. Water is a polar molecule (hydrogen bond!)

Water can dissolve some substances (salts) but

cannot dissolve membranes

Solar energyfrom hydrogen fusion

Temperature

Electromagnetic Radiation(waves)

How far from the star should anEarth-like planet be to maintain

liquid water on its surface?

Habitable ZoneA circumstellar habitable zone (HZ) is defined as aregion around any star where a planetary body can

maintain liquid water on its surface

Under the present Earth’s atmospheric pressure (1 atm = 101325 Pa) water is stable if the temperature is

273K < T < 373K

On a planetary surface temperature (T) is key

…assuming the planet has some atmosphere!

We must determine the Planet’s

Planetary Energy Budget

absorbed energy = emitted energy

How do we determine a Planet’s surface temperature?

Total amount of energy reaching the Earth is given by the amount of radiation hitting an area corresponding to the disk of the Earth: A=πr2

Ein

re

Incoming EnergyHow much solar energy gets to the Earth?

2E0in rSE π

A

How much solar energy is absorbed by the Earth’s surface?

Some energy is reflected away

Fraction of incident sunlight that is reflected

Range: 0 – 1 (no reflection) (100% reflection)

Typical Surface Albedos: Sand – 0.2-0.4 Forest – 0.08-0.18 Green grass – 0.25 Ocean – 0.03-0.06 Fresh Snow – 0.8-0.9

Average Earth’s albedo: a = 0.30

Albedo

Absorbed Energy

The amount of absorbed energy is given by the amount of incident energy minus the amount of reflected energy:

Eabs = Ein – Erefl

or

Eabs = Ein – aEin

Eabs = Eout

(1-a)Ein = Eout

Energy Balance

absorbed energy = emitted energy

2E0 rS

Eout

Ein

aEin

Energy Balance

The amount of energy absorbed by the Earth is equal to the energy emitted (Eout) by the Earth

Otherwise, the Earth’s temperature would continually rise (or fall)

We can use Stefan-Boltzmann to calculate the amount of

energy radiating from the Earth

How do we determine the Energy emitted by the Earth?

4σTF F = flux of energy (W/m2)T = temperature (K) = 5.67 x 10-8 W/m2K4 (constant)

Total energy emitted by the Earth

Start from Stefan-Boltzmann’s law:

F = T4 [W/m2]

But! This is a flux, energy per unit area, not total energy

We must multiply the flux by an area (area of the Earth’s surface)

Eout = σT4 AEarth

Eout

Ein

aEin

2E0abs ra)S(1E

2E

4Earth

4out r4σTAσTE

rE

Putting It All Together:

Energy Balance: Eabs = Eout

Eout

Ein

aEin

2E

42E0 r4σTra)S-(1

40 σTa)S-(1 4

Energy Balance: Eabs = Eout

Eout

Ein

aEin

4σ

a)S(1-T 04

em

So = 1370 W/m2

a = 0.3 = 5.67 x 10-8 W/m2K4

Earth Surface Temperature

4σ

a)S(1-T 04

em

428-

24em

KmW105.674

mW13700.3)(1-

T

494em K104.23T

K104.23T 9em

4

255KTem

What does it correspond to in °C and °F?

We expect an average surface temperature (emission temperature) of:

Earth’s Average Surface Temperature

NO, the actual temperature is warmer!

Is the Earth’s surface at 255K?

The average observed temperature at the Earth’s surface is:

Tobs = 288K (or +15oC, +59oF)

Difference between observed and expected temperatures:

T = Tobs – Tem = 288K– 255K

T = + 33K = 33°C = 59.4°F

What did we do wrong?

Earth Surface Temperature

We must consider the interaction of atmospheric gases with the incoming and

outgoing radiation

Natural Greenhouse Effect

Original Greenhouse

Precludes heat loss by inhibiting the upward air motion

Solar energy is used more effectively: Same solar input higher temperatures

Atmospheric Greenhouse Effect

Incoming Solar Radiation

N2, O2, Ar

Greenhouse gases (e.g., CO2, H2O)

Outgoing IR Radiation

Earth’s Surface

Reflected

Composition of the Atmosphere

Air is composed of a mixture of gases:

Gas Concentration (%)

N2 78O2 21Ar 0.9H2O variableCO2 0.037 370 ppmCH4 1.7N2O 0.3O3 1.0 to 0.01 (stratosphere - surface)

greenhousegases

99.9%Non-greenhouse

Greenhouse Gases

C OOcarbon dioxide

HO

Hwater

methane

H

C H

H

H OO+

-Oozone

Non-greenhouse Gases

nitrogen oxygenN N O O

Electron cloud is distributed equally over the atoms in the molecule

(Technically speaking, greenhouse gases have a dipole moment whereas N2 and O2 don’t)

Molecules with an uneven distribution of electrons are especially good absorbers and emitters

These molecules are said to be dipoles

O

H

H

WaterElectron-poor region:Partial positive charge

Electron-rich region:Partial negative charge

oxygen is more electronegative than hydrogen

(+)

(+)

(-)

Molecules of greenhouse gases absorb energy from radiation

The energy increases the movement of the molecules, including vibration and rotation

The molecules gain kinetic energy that may then be transmitted to other molecules such as oxygen and nitrogen and cause a general heating of the atmosphere

Greenhouse gases and radiation

CO2 Vibration

CO2 bending mode

- Absorption of radiation (around 15 μm)

- Bending of molecule and emission of IR

Wavelength: 15 m 7.2 m 4.2 m

H2O Vibration

Absorption wavelengths:

2.7 m 2.6 m 6.2 m

Librations (liquid water only)

Molecular Rotation

Slow Rotation Rate Faster Rotation Rate

Incoming radiation

Involves wavelengths in the microwave (>1,000 m!)

Solar Spectrum at Earth’s SurfaceGreenhouse gases absorb IR radiation at specific wavelengths

CO2

Quiz Time !