1. Major Concepts of Physics PHY102 – Lecture #10 1 2016  Syracuse University Lecture #10 Do cold solids emit light? February 24 th Spring 2016 Prof. Liviu Movileanu http://movileanulab.syr.edu/MajorConceptsPhysics2016.html lmovilea@syr.edu Room 211, Physics Bldg., 443-8078 Major Concepts of Physics PHY102

2. Major Concepts of Physics PHY102 – Lecture #10 2 2016  Syracuse University 1. Blackbody radiation. Experimental evidence 2. Stefan-Boltzmann’s law 3. Continuous spectrum produced by the solids 4. Lecture demonstration (Blackbody radiation) 5. Wien’s law 6. Announcements/Homework Lecture objectives

3. Summary of the observations: 1. A filament (made of tungsten) was heated until it began to glow. 2. As the temperature T was increased further, the total intensity of light emitted increased. 3. The infrared radiation intensity (heat) also increased, as T increased. Major Concepts of Physics PHY102 – Lecture #10 3 2016  Syracuse University Observations - Workshop

4. Major Concepts of Physics PHY102 – Lecture #10 4 2016  Syracuse University Electromagnetic waves - Summary

5. Major Concepts of Physics PHY102 – Lecture #10 5 2016  Syracuse University Intensity of radiation versus frequency

6. Major Concepts of Physics PHY102 – Lecture #10 6 2016  Syracuse University Intensity of radiation versus wavelength

7. Major Concepts of Physics PHY102 – Lecture #10 7 2016  Syracuse University UV, IR and Visible 1) Stefan-Boltzmann law 2) Continuous spectrum produced by the solids 3) Wien Law 4) Examples 5) Textbook

8. Boltzmann’s Law Major Concepts of Physics PHY102 – Lecture #10 8 2016  Syracuse University THE following colors were produced, in succession, as T increases: Red; Red-Orange; Yellow; White. History In 1884, Boltzmann postulated a law on the total radiation- rate emitted by a black body: ∆Q/∆t =  AT 4 ∆Q is the total radiation emitted in the time interval ∆t. A is the area of the blackbody that is emitting radiation. T is the absolute temperature. The symbol  is a universal constant.

9. Major Concepts of Physics PHY102 – Lecture #10 9 2016  Syracuse University Stefan, later, did experiments that confirmed this relation. He also found the value of  to be 5.7 x 10 -8 W/m 2 K 4. This relation is called the Stefan-Boltzmann Law. It is in qualitative accord with your experiments that you will conduct in the Workshop. Stefan-Boltzmann Law

10. Major Concepts of Physics PHY102 – Lecture #10 10 2016  Syracuse University The relation gives the total radiation produced. What about the wavelengths of radiation produced at any given T ? Wavelength Dependence Red is the first color to appear when the solid begins to glow. This occurs at about T = 800K. First conclusions: At room temperature, solids do not produce detectable amounts of light. At higher temperatures, starting at about 800K, red light is produced. This continues to about 1200K. A red color is seen, in this range of T. Nature of Red Light Red is a primary color. That is, red light is an electromagnetic wave with just one value for its wavelength. Stefan-Boltzmann law

11. Further, it has the longest wavelength (about 680 nm) of all visible light. So, experiment indicates: The lowest temperature (for visible light) results in the longest wavelength emitted. Raise T above 800K. At about T = 1,800K, the color changes to red-orange (from red). Note: Orange has the second longest λ in the visible spectrum. Conclude: Result of increase of T is that shorter wavelengths of light are produced. Note: Red and orange are produced simultaneously. Major Concepts of Physics PHY102 – Lecture #10 11 2016  Syracuse University Red-Orange Transition

12. Conclude: Solids produce a continuous range of wavelengths. You see a continuous range of colors. Raise T to 2000K. The color that appears is yellow. When is yellow perceived to be the color? Yellow is a primary color, (λ can be anywhere from 620 nm to 540 nm). Major Concepts of Physics PHY102 – Lecture #10 12 2016  Syracuse University Continuous spectrum

13. The perception of yellow also occurs when red and green enters the eye with roughly equal intensities. Conclusion: At T = 2000K, light is produced of all wavelengths between red (670 nm) and green (470 nm). The perception is yellow for two reasons: a) The red light and green light combine to give yellow. b) Yellow as a primary color is produced. This adds to the sensation of yellow.. Major Concepts of Physics PHY102 – Lecture #10 13 2016  Syracuse University Sensation of Yellow

14. While red and green are produced in prodigious amounts, blue and violet dominate, and the color that appears is blue. Note that the Wien’s law allows us to estimate the surface temperature of a star, by simply observing the dominant colors it emits. Note: As T increases, λ max decreases. This will agree with your observations during this week’s workshop. To summarize so far, Wien’s law explains why the observed colors go from red to red-orange, to yellow, as T is increased. Still larger T At about 2,400K, and higher, the color becomes white. Why? Wien’s Law provides the explanation. Example: T = 6000K, the temperature at the surface of the sun. Major Concepts of Physics PHY 102 – Lecture #10 14 2016  Syracuse University Wien’s law

15. For increasing temperatures, the black body intensity increases for all wavelengths. The maximum in the energy distribution shifts to shorter (longer ) for higher temperatures. max T = 2.9x10 -3 m K is Wien’s law for the maximum I providing an estimate of the peak emission ( max =517.5 nm for the Sun). Wien’s displacement law Major Concepts of Physics PHY102 – Lecture #10 15 2016  Syracuse University

16. Major Concepts of Physics PHY 102 – Lecture #10 16 2016  Syracuse University

17. Major Concepts of Physics PHY 102 – Lecture #10 17 2016  Syracuse University

18. Major Concepts of Physics PHY102 – Lecture #8 20 2005  Syracuse University

19. Major Concepts of Physics PHY 102 – Lecture #10 19 2016  Syracuse University Colors from the Sun Calculate λ max from Wien’s law. T = 6,000K Result: 480 nm. The wavelength 480 nm is in the green (middle) part of the spectrum. Conclude: At 6000K, the radiation produced is a mixture of red, green and blue light, with intensity peaked in the green. But: The eye perceives equal intensities of red, green and blue as white light. This explains why white light is perceived at the highest temperatures.

20. Suppose that we increase the temperature still further. At 8000K, the value of λ max is in the blue part of the visible spectrum. Stars whose surface temperature is more than 8000K are called blue-hot stars. Major Concepts of Physics PHY 102 – Lecture #10 20 2016  Syracuse University Blue-Hot Stars

21. Major Concepts of Physics PHY102 – Lecture #10 21 2016  Syracuse University Good absorbers are good emitters. Good reflectors are poor emitters. Emissivity of a Solid The emissivity, e, of a solid measures the ability of the solid to emit radiation at a given temperature T. For a perfect black body, e = 1. For a perfect reflector, e = 0. Stefan-Boltzman’s law Recall the law: For a black body, area A, at temperature T: P = ∆Q/∆t =  AT 4 Its extension for a general solid: Insert the factor e on the right side of the law: ∆Q/∆t = e  AT 4 Emissivity of a solid

22. Major Concepts of Physics PHY 102 – Lecture #10 22 2016  Syracuse University What is white light?/Newton’s observation

23. The dispersion of light Major Concepts of Physics PHY 102 – Lecture #10 23 2016  Syracuse University Conclusion: White light is a composite of the primary colors. Prism reveals this by separating them out. The experiment is: the dispersion of light. Later discovery: Each primary color has its own wavelength range. The shortest wavelengths are bent the most. Violet light (shortest wavelength) is bent the most. Red light (longest wavelength) is bent the least.

24. Major Concepts of Physics PHY102 – Lecture #10 24 2016  Syracuse University 1.Reading 1.Reading: Chapter 14 th, Section 14.8, pp. 521-527 Conceptual examples 14.12, 14.13, 14.14, 14.15, 14.16 2. Homework 2. Homework for the next week: The homework #4 is now posted online. This HW is due on next week’s workshop. 3. This week’s laboratory. Blackbody radiation. Announcements