Major Concepts of Physics PHY102 – Lecture #  Syracuse University Lecture #8 Do solids emit light? February 11 th Spring 2015 Prof. Liviu Movileanu Room 211, Physics Bldg., Major Concepts of Physics PHY102

Major Concepts of Physics PHY102 – Lecture #  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

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 #  Syracuse University Observations - Workshop

Major Concepts of Physics PHY102 – Lecture #  Syracuse University Electromagnetic waves - Summary

Major Concepts of Physics PHY102 – Lecture #  Syracuse University Intensity of radiation versus frequency

Major Concepts of Physics PHY102 – Lecture #  Syracuse University Intensity of radiation versus wavelength

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

Boltzmann’s Law Major Concepts of Physics PHY102 – Lecture #  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 α is a universal constant.

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

Major Concepts of Physics PHY102 – Lecture #  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

Stefan – Boltzmann Law Blackbody radiation is continuous and isotropic whose intensity varies only with wavelength and temperature. Following empirical (Josef Stefan in 1879) and theoretical (Ludwig Boltzmann in 1884) studies of black bodies, there is a well known relation between the Radiation Flux and the Temperature known as Stefan-Boltzmann law: F=aT 4 F= Radiation flux=  Q/ (  tA)  t = time; A = surface area Major Concepts of Physics PHY102 – Lecture #  Syracuse University

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, color changes to red-orange (from red). Note: Orange has the second longest λ in the visible. Conclude: Result of increase of T is that shorter wavelengths of light are produced. Note: Red and orange are produced simultaneously. 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, color changes to red-orange (from red). Note: Orange has the second longest λ in the visible. 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 #  Syracuse University Red-Orange Transition

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? The Two Yellows Yellow is a primary color, (λ can be anywhere from 620 nm to 540 nm). Major Concepts of Physics PHY102 – Lecture #  Syracuse University Continuous spectrum

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 #  Syracuse University Sensation of Yellow

Experiments on the Wavelengths Emitted---Done in the 1890s Result: At any fixed T, there is always a continuous curve giving the intensity I versus the wavelength λ. The curve always has one value for λ (denoted as λ p ) at which I is peaked. λ p depends on T. Wien’s Law From experiment, λ p is given by the relation (Wien’s Law): λ p T = 2.9 x m K. Note: As T increases, λ p 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 PHY102 – Lecture #  Syracuse University Wien’s Law

For increasing temperatures, the black body intensity increases for all wavelengths. The maximum in the energy distribution shifts to shorter (longer ) for higher temperatures. p 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 #  Syracuse University

Major Concepts of Physics PHY102 – Lecture #  Syracuse University

Major Concepts of Physics PHY102 – Lecture #  Syracuse University

Major Concepts of Physics PHY102 – Lecture #  Syracuse University 1.Reading 1.Reading: Chapter 14 th, Section 14.8 (on PHY 102 Web- page) Conceptual examples 14.12, 14.13, 14.14, Homework 2. Homework for the next week (on paper): The homework #3 is now posted online. This HW is due on next week’s workshop. 3. Reading materials 3. Reading materials are provided online (see the PHY 102 web page) and on paper provided in class.Announcements