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:  Useful Reading: class website  “Reading Material” 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 energy from hydrogen fusion Temperature Electromagnetic Radiation (waves) How far from the star should an Earth-like planet be to maintain liquid water on its surface?

Habitable Zone A circumstellar habitable zone (HZ) is defined as a region around any star where a planetary body can maintain liquid water on its surface Under the present Earth’s atmospheric pressure (1 atm = 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= πr 2 E in rere Incoming Energy How much solar energy gets to the Earth? 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 – Forest – Green grass – 0.25 Ocean – Fresh Snow – 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: E abs = E in – E refl or E abs = E in – aE in

E abs = E out (1-a)  E in = E out Energy Balance absorbed energy = emitted energy

E out E in aE in Energy Balance The amount of energy absorbed by the Earth is equal to the energy emitted (E out ) 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? F = flux of energy (W/m 2 ) T = temperature (K)  = 5.67 x 10-8 W/m 2 K 4 (constant)

Total energy emitted by the Earth Start from Stefan-Boltzmann’s law: F =  T 4 [W/m 2 ] 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) E out = σT 4  A Earth

E out E in aE in rErE Putting It All Together:

Energy Balance: E abs = E out E out E in aE in

Energy Balance: E abs = E out E out E in aE in

S o = 1370 W/m 2 a = 0.3  = 5.67 x W/m 2 K 4 Earth Surface Temperature

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: T obs = 288K (or +15 o C, +59 o F) Difference between observed and expected temperatures:  T = T obs – T em = 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 N 2, O 2, Ar Greenhouse gases (e.g., CO 2, H 2 O) Outgoing IR Radiation Earth’s Surface Reflected

Composition of the Atmosphere Air is composed of a mixture of gases: Gas Concentration (%) N 2 78 O 2 21 Ar0.9 H 2 Ovariable CO ppm CH N 2 O 0.3 O to 0.01 (stratosphere - surface) greenhouse gases 99.9% Non-greenhouse

Greenhouse Gases COO carbon dioxide H O H water methane H CH H H O O + - O ozone

Non-greenhouse Gases nitrogen oxygen N O Electron cloud is distributed equally over the atoms in the molecule (Technically speaking, greenhouse gases have a dipole moment whereas N 2 and O 2 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 Water Electron-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

CO 2 Vibration CO 2 bending mode - Absorption of radiation ( around 15 μm ) - Bending of molecule and emission of IR Wavelength: 15  m7.2  m 4.2  m

H 2 O Vibration Absorption wavelengths: 2.7  m 2.6  m 6.2  m Librations (liquid water only)

Molecular Rotation Slow Rotation RateFaster Rotation Rate Incoming radiation Involves wavelengths in the microwave (>1,000  m!)

Solar Spectrum at Earth’s Surface Greenhouse gases absorb IR radiation at specific wavelengths CO 2

Quiz Time !