Mechanics:
Heat and Thermodynamics (Macroscopic Large Scale Phenomena)
Kinetic Theory ( Statistical mechanics) ( Microscopic Small Scale Phenomena)
Average over microscopic properties give rise to macroscopic properties
Eg. Temperature is a measure of the average molecular kinetic energy. Pressure is average force on wall of container due to molecular collisons.
Electromagnetic Theory: Maxwell and the Wave Equation.
Radiation: Classically due to oscillating charge dipoles. Radiation from oscillators cause heat transfer through EM waves. Radiation transfer occur at all non zero Temperature T and is in the infra red part of the EM spectrum.
At thermal equilibrium the black body radiates and also absorbs at the same rate and the spectrum of radiation is
continuous and depends on the temperature T and the nature
of the material.
The power radiated by a black body is given by the Stefan-Boltzmann Law as
P=e σ A (T4 -T04)
where T0 is the ambient temperature, e is the emissivity and σ is the Stefan constant. By Kirchoff's Law e=a at thermal equilibrium where a is the absorptivity of the body. For an ideal black body radiator e=a=1 and the spectrum is universal and dependent only on the temperature.
A graphite cavity with thick walls and a small hole may be approximated to
an ideal black body such that it is perfect absorber and absorbs all radiation incident on it. The cavity walls re radiate and at thermal equilibrium the cavity is full of radiation at te ambient temperature T. If this cavity is heated to T then the hole must radiate like a black body by Kirchoffs Law because a perfect absrober
is also a perfect emitter. So the radiation from the hole may be understood by analysing the cavity radiation.
The energy density ( energy/volume) of the cavity radiation ρT(ν) is proportional to RT(ν) where R is the spectral radiancy (energy radiated/unit time/unit area) of the black body. A graph of the spectral radiancy was
obtained by Lummer and Pringsheim at various temperatures in deg K through experiemnets.
Spectral Radiancy Curves with Frequency
Image From: thermal-survey.co.uk via Google Images
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The characteristics of these curves are
1. Very little power radiated for low frequency P=0 for ν=0
2. Increases with increase in frequency and reaches a maxima for νmax
3. Drops with further increase and asymptotes to zero for ν infinity.
4. The peak frequency νmax shifts to higher frequecies for higher temperatures.
The total radiancy RT=∫ RT(ν) dν=σ T4
Wiens Law: W=T λmax where W is the Wien's constant. This is
a theoretical fit to an experimental curve and the value of W is thus obtained.
