UMKC, Department of Physics 1 of 3 Modern Physics – Stefan-Boltzmann

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Physics 476LW Advanced Physics Laboratory

Stefan-Boltzmann Introduction The problem of blackbody radiation was one of the central sticking points of classical physics. Each time an explanation of the phenomena was proposed experimental results showed it to be inadequate. The problem was especially difficult when considering the thermal radiation analyzed over all wavelengths of light. In this experiment we will only consider the aggregate case. Theory Thermal radiation was defined by Maxwell as when "the hot body loses energy and the cold body gains energy by some process occurring in the intervening medium, which does not itself thereby absorb energy." If the intervening medium is vacuum or a gas consisting of symmetric molecules, then it can be considered to be "thermally transparent". However, if the medium consists of non-symmetric molecules such as H2O or CO2 energy may be strongly absorbed at some wavelengths. [1] The rate at which an object radiates energy is proportional to the fourth power of its absolute temperature. This is known as Stefan's law and is expressed as

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P =σAeT 4 where P is power in watts, A is the area of the object in square meters, e is the emissivity of the object which depends on the character of the object, T is the temperature in kelvins, and σ is a constant known as the Stefan-Boltzmann constant. As an object radiates energy it also absorbs energy from its surroundings otherwise it would eventually radiate all its energy and reach absolute zero. So, if an object is at temperature T and its surroundings are at an average temperature T0, then its net rate of energy change is given by

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Pnet =σAe(T 4 −T04 )

An object which absorbs all of the energy which falls on it is called an ideal absorber or blackbody. For such a body e = 1. In this experiment we will determine the constant σ which is referred to as the Stefan-Boltzmann constant. For more information see [6] or [7].

UMKC, Department of Physics 2 of 3 Modern Physics – Stefan-Boltzmann

Experimental Apparatus and Procedures Apparatus The apparatus is the Laws of Radiation apparatus supplied by Klinger Educational Products with local modifications. The system consists of an electric oven that heats a burnished brass cylinder 3.5 cm in diameter by 10 cm long. The oven has a 2.9 cm hole in one end for emission of radiation and a 1.2 cm hole in the other end for the temperature probe. The temperature probe is a NiCr-Ni sensor with a digital thermometer. The oven is powered by a Powerstat variable autotransformer that is connected through a safety box. The oven is shielded by a water cooled blackbody accessory with a 1.7cm opening. The power is measured by a Scientech 361 power meter and sensor. The oven, temperature probe, blackbody accessory, and power meter sensor are all mounted on a graduated rail. Procedure First, check to see that all the electrical components are plugged in. Set the digital thermometer selector switch to "<200°C". Turn on the cooling water. Set the power meter selector dial to .03 and zero the meter for ambient conditions. Record the ambient temperature. Switch on the transformer and the safety box. Set the transformer to 120 V. As the temperature increases we record the temperature and power meter readings at 25°C intervals when the temperature exceeds 200°C you will need to change the thermometer selector switch to ">200°C". When the temperature reaches a value between 350°C and 400°^C rotate the transformer dial to zero and switch it off. Then record temperatures and power meter readings at 25 degree intervals as the temperature falls back to room temperature. Since we must account for both the energy emitted by the blackbody and the energy absorbed by the body we use the value T4 - T0

4 to calculate the Stefan-Boltzmann constant. Also, we must calculate power per unit area and account for the emissivity of the burnished brass. For this experiment e = 0.61. [5]. Conclusions Make plots of your data and compute the Stefan-Boltzmann constant. Discuss sources of error and do an error analysis. [1] M. Sprackling, Thermal Physics (American Institute of Physics, New York, New York 10025, 1991). [2] A. dAbro, The Rise of the New Physics (Dover Publications, Mineola, New York 11501, 1951). [3] G. Gamow, Thirty Years That Shook Physics (Dover Publications, Mineola, New York 11501, 1966). [4] E. Weisstein, ed. Eric Weisstein's World of Physics (World Wide Web, http://scienceworld.wolfram.com/physics/, 2007). [5] D. R. Lide, ed. CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, FL, 1993). [6] Serway and Jewett, Physics for Scientists and Engineers (Thomson, Brookw/Cole, Pacific Grove, CA, 2003). [7] Tipler and Llewellyn, Modern Physics (Freeman, NY, NY, 2003)

UMKC, Department of Physics 3 of 3 Modern Physics – Stefan-Boltzmann

Scientech 361 power meter Scientech 361 power meter sensor

Digital thermometer sensor Digital thermometer

Oven and accessory shield Variable autotransformer

Safety box All components assembled