Energy, Power and Climate Change

1. Energy, Power and Climate Change Wien’s Law and Stefan-Boltzmann Law

2. Black-body Radiation • Radiation given out from a hot object depends on many things. • Black-body radiation is the radiation emitted by a “perfect emitter” - a perfect emitter emits all the radiation that it absorbs • A perfect emitter is also a perfect absorber - a black object absorbs all of the light energy falling on it.

3. Black-body radiation depends on temperature - each temperature has a range of emitted wavelengths

4. Wien’s Law Relates wavelength to surface temperature 0T = constant = 2.90 x 10-3 K m Equation in Astrophysics Option E of Reference Table

5. Wien’s Law Example: • The sun has an approximate black-body spectrum with most of the energy radiated at a wavelength of 5.0 x 10-7 m. Find the surface temperature of the sun.

6. Radiation from Stars • Surface temperature is much less than the core temperature • Hot stars emit all frequencies of visible light and will tend to appear white • Cooler stars emit higher wavelengths and appear red • Radiation from planets peaks in the infrared range

7. Radiation from Matter • All objects above absolute zero radiate electromagnetic waves • Radiation is in the infrared range for everyday objects • At constant temperature, rates of absorption and radiation are the same • A good radiator is a good absorber

8. Radiation from Matter (continued) • Surfaces that are light in color and smooth (shiny) are poor radiators and poor absorbers (ex - wear white in summer) • Dark and rough surfaces are good radiators and good absorbers • As temperature increases, rate at which energy is radiated also increases • Radiation can travel through a vacuum (space)

9. Stefan-Boltzmann Law • Relates total power radiated (luminosity) by a black body (per unit area) to temperature where T4 is proportional to total power radiated • = Stefan-Boltzmann constant = 5.67 x 10-8 W m-2 K-4 A = 4πR2 (surface area)

10. Example: • The sun (radius = 7.0 x 108 m) radiates a total power of 3.9 x 1026 W. Find its surface temperature. T = 5781K

11. Equilibrium • Constant temperature - power absorbed equals rate at which energy is radiated - thermal equilibrium • If more energy is absorbed than radiated, temperature goes up • If more energy is radiated than absorbed, temperature goes down

12. Emissivity • Emissivity - ratio of power radiated by an object to power radiated by a black body at the same temperature

13. Surface Heat Capacity Cs • Energy required to raise the temperature of a unit area on a planet’s surface by one degree • measured in J m-2 K-1

14. Total Power Absorbed • Total power absorbed by planet: Where: r = planet radius P = power received per unit area  = albedo Remember albedo? This is the fraction of the radiation that is reflected back into space before it reaches the Earth’s surface!

15. Total Power Radiated • Total power radiated from the surface of a planet (Stefan-Boltzmann Law and concept of emissivity) • Total power radiated:

16. So…at equilibrium: • Total power absorbed = total power radiated: Temperature at equilibrium:

17. What if we don’t have equilibrium? • If incoming radiation power and outgoing radiation power are not equal, we have a temperature change. • Temperature of a planet can be predicted • Assumptions: • Planet’s variations in temperature due to interactions are ignored • Changes that occur due to temperature change are ignored (ex. changes in albedo or emissivity)

18. Calculating Temperature Change: