1. Sayfa 1 Department of Engineering Physics University of Gaziantep June 2014 Topic X BLACKBODY RADIATION EP324 Applied Optics

2. Sayfa 2 Introduction  If you turn on an electric stove, the stove plate heats up until it becomes red or orange hot.  The red glow that you see consists of photons with energies in the visible red range.  When the stove plate was cold, it also emitted photons, but those were of too low energy to be seen by our eyes.

3. Sayfa 3  All objects radiate energy continuously in the form of electromagnetic waves produced by thermal vibrations of the molecules.  The characteristics of this radiation depend on the temperature and properties of the object’s surface.  Every second, approximately 1370 J of electromagnetic radiation from the Sun passes perpendicularly through each 1 m 2 at the top of the Earth’s atmosphere.

4. Sayfa 4 Stefan’s Law The rate at which an object radiates energy is proportional to the fourth power of its absolute temperature: P = power in watts of electromagnetic waves radiated from the surface. σ = 5.6696 x 10 –8 W/m 2. K 4 A = surface area T = surface temperature in kelvins. e= emissivity or absorptivity (0<e<1). for perfect mirror e = 0 for black body e = 1

5. Sayfa 5 EXAMPLE Two lightbulbs have cylindrical filaments much greater in length than in diameter. The evacuated lightbulbs are identical except that one operates at a filament temperature of 2 100°C and the other operates at 2 000°C. Find the ratio of the power emitted by the hotter lightbulb to that emitted by the cooler lightbulb.

6. Sayfa 6 An object radiates energy: It also absorbs electromagnetic radiation from the surroundings: Net rate of energy gained or lost:

7. Sayfa 7 Black Body Radiation From a classical viewpoint, thermal radiation originates from accelerated charged particles in the atoms near the surface of the object; Black body is an ideal system that absorbs all radiation incident on it. The electromagnetic radiation emitted by the black body is called blackbody radiation.

8. Sayfa 8 Cavity A good approximation of a black body is a small hole leading to the inside of a hollow object.

9. Sayfa 9 Black Body Spectrum When a black body heated a distribution of wavelength is observed.

10. Sayfa 10 Black Body Spectrum Intensity of blackbody radiation versus wavelength at three temperatures. The amount of radiation emitted (the area under a curve) increases with increasing temperature.

11. Sayfa 11 Black Body Spectrum u(λ) spectral distibution function Rule 1: Rule 2 (Wein’s displacement law) : The peak of the wavelength distribution shifts to shorter wavelengths as the temperature increases.

12. Sayfa 12 See lecture notes for details. http://en.wikipedia.org/wiki/Thermal_radiation Plank’s Formula

13. Sayfa 13 EXAMPLE Using Plank’s formula for a black-body radiator, derive Wein law: or Hint: Plank formula is given by: use dimensionless variable: and solve http://en.wikipedia.org/wiki/Thermal_radiation

14. Sayfa 14 Quiz

15. Sayfa 15 This thermometer is very sensitive because temperature is raised to the fourth power in Stefan’s law. Ear Thermometer

16. Sayfa 16  Blackbody radiation is the radiation emitted by a black surface that is in thermal equilibrium.  Planck’s blackbody spectrum determines how much is radiated at each frequency.  Surfaces that are not black emit radiation that is less by a factor called the emissivity.  Emissivity equals absorptivity for the same frequency and direction of radiation. Key Points

17. Sayfa 17 References [1]. http://www.mathworks.com/products/matlab [2]. Numerical Methods in Engineering with MATLAB, J. Kiusalaas, Cambridge University Press (2005) [3]. Numerical Methods for Engineers, 6th Ed. S.C. Chapra, Mc Graw Hill (2010)