Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Thermodynamic system wikipedia , lookup
Equipartition theorem wikipedia , lookup
Second law of thermodynamics wikipedia , lookup
History of thermodynamics wikipedia , lookup
Internal energy wikipedia , lookup
Conservation of energy wikipedia , lookup
Heat transfer physics wikipedia , lookup
Black-body radiation wikipedia , lookup
THE ORIGINS OF QUANTUM MECHANICS 1-BLACKBODY RADIATION. Blackbody radiation is a common phenomenon that probably is familiar to you. When you see stars of different colors, when you observe an electric heating coil on a stove turn red, or when you observe a lightbulb, you are observing blackbody radiation. A blackbody is a device that converts heat into radiant energy. Heating an object to different temperatures causes that object to radiate energy of different wavelengths and therefore, different colors E.g. Heating a steel color changes by increasing temperature Color depends only on temperature Not on type of material Color observed due to characteristic distribution of light emission at a range of wavelengths If you know the color you know the temperature 1 The best laboratory black-body is a spherical cavity which is constructed with insulating walls in one of which a small pinhole is made. Classical (Rayleigh-Jeans) ( , ) = 5000 = 4000 = 3000 When black-body heated it is observed to radiate a spectrum of wavelengths having a characteristic energy density at each frequency. (Draw the spectrum with ) Classical Explanation (Rayleigh-Jeans law) They supposed that 1. Blackbody radiation is coming from standing electromagnetic waves in the cavity that are in thermal equilibrium with the vibrating atoms (or electrons) in the walls 2. The atoms in the blackbody are assumed to vibrate like harmonic oscillators 3. according to the principle of equipartition of energy an oscillator in thermal equilibrium with its environment should have an average energy equal to kT 4. We already found out that ( = ) for standing waves in sphere from classical physics 5. the energy density is ( ) and so the relationship between the energy density and the frequency of the radiation is (for unit volume) Where ( ) = ( 2 8) is the energy density in units of energy per volume (e.g., J m-3), is the frequency of emitted radiation, T is the temperature of the blackbody, k is Boltzmann's constant, and c is the speed of light. This is known as the Rayleigh-Jeans law. A clear implication of this law is that as the frequency becomes larger, the energy density increases as the square of the frequency. This is known as the "ultraviolet catastrophe", (why) No maximum energy density Short wavelengths strongly excited Everything glows at room temperature? Long Wavelengths Works OK. CLASSICAL THEORY FAILS new theory is required Quantum Explanation (Max Planck) Max Planck started from the standard assumption, that 1. blackbody could be modeled as a collection of oscillators 2. He then made an assumption that the oscillators could only take on discrete, quantized energies, these energies being described as where n is the oscillator energy, is a whole number (0, 1, 2, ...), is the frequency, and is some arbitrary constant having units of (energy h time). 3. With this assumption, and using Boltzmann distribution law , Planck derived ( ) = ( 3 1) at low frequencies using the series expansion for the exponential / 1+ we recover the Rayleigh-Jeans formula. 8 ( , ) = At high frequencies / ( , ) = 1 8 / the exponential dominates the cubic in and so goes to zero. So using quantization is required, for correct behavior at high frequencies. (Energy is quantized) The constant h has come to be called Planck's constant, and its value is 6.626 x10-34 J s. Expression of the energy density ( , ) in terms of wavelength ( , ) 8 ( , ) = ( / 1) ( , ) = = ( = 8 / 1) Wien displacement law He states that the wavelength distribution of thermal radiation from a black body at any temperature has essentially the same shape as the distribution at any other temperature, except that each wavelength is displaced on the graph. He states that if max is the wavelength at which ( , ) is a maximum, and so ( , ) = ( 4 8 / 1) =0 By differentiation of the above equation with respect to and substitution by the constants value (h, c , k) it is found that = 2.897 10 Example: calculate the temperature used to heat a black body to emit radia on at 400 nm 2.897 10 2.897 10 = = = 7242.5 400 10 Stefan–Boltzmann law The law states that the total energy radiated per unit surface area of a black body per unit time (also known as the black-body irradiance or emissive power), P, is directly proportional to the fourth power of the black body's thermodynamic temperature T. = Where = 5.6697 10 By integration the Plank's law to get the total energy density so 8 ( , ) = = ( / 1) = 8 15 The relation between the emissive power and the total energy density is = 4 2 15 = 4 4 = 2 15 2 = 15 By substitution by the constants value ( , h, c , k) it is found that = 5.670 10 = Example: Calculate the intensive power of the above black body 5