Bodies: black between

In this chapter, the foundations of equilibrium statistical mechanics are introduced and applied to ideal and weakly interacting systems. The coimection between statistical mechanics and thennodynamics is made by introducing ensemble methods. The role of mechanics, both quantum and classical, is described. In particular, the concept and use of the density of states is utilized. Applications are made to ideal quantum and classical gases, ideal gas of diatomic molecules, photons and the black body radiation, phonons in a hannonic solid, conduction electrons in metals and the Bose—Einstein condensation. Introductory aspects of the density... 

Consider radiative exchange between a body of area A i and temperature Ti and black surroundings at To. The net interchange is given by... 

A plate. 1 m in diameter at 750 K, is to be heated by placing it beneath a hemispherical dome of the same diameter at 1200 K the distance between the plate and the bottom of the dome being 0.5 m, as shown in Figure 9.42. If the surroundings are maintained at 290 K, the surfaces may be regarded as black bodies and heat transfer from the underside of the plate is negligible, what is the net rate of heat transfer by radiation to the plate ... 

Fig. 3.21 Example of temperature variation as measured by MIMOS II temperature sensors on MER (i) inside the rover body at MIMOS electronics board (black curve), (ii) outside the rover, at the MIMOS II SH (green and red curves), which is at ambient Martian temperature (a) inside the sensor-head, at the reference absorber position (green), (b) outside the SH at the sample s contact plate (red). Temperatures at the two SH positions are nearly identical (difference less than 2 K). During data transmission between the rover and the Earth (or the relay satellite in Mars orbit) the instrument is switched off resulting in immediate small but noticeable temperature changes (see figure above)...

Note the potential confusion between luminosity of the Sun L and the flux at the Earth. The latter is quite naturally written as the amount of radiation arriving on every square metre of the Earth s surface and analogously the flux per square metre from the black body is also F. This calculation requires the total amount of radiation emitted by the Sun to be known, which is the luminosity of the Sun and not its flux. 

Detectors with complete black body rejection capability are usually less sensitive to fires than a single frequency infrared optical detector. Because it s discrimination of fire and non-fire sources depend upon an analysis of the ratio between fire and reference frequencies, there is a variation in the amount of black body rejection achieved. A detector s degree of black body radiation rejection is in inversely proportion to its ability to sense a fire. The detectors are limited to applications that involve hydrocarbon materials. 

An average of temperature records on the earth s surface over a year indicates that the earth s average surface temperature is about 14°C (57°F). But, the earth s 240 watts per square meter of thermal infrared radiation as measured by satellite is equivalent to the radiation emitted by a black body whose temperature is about -19°C (-3°F), not the 14°C (57°F) average measured at the earth s surface. The 33°C (60°F) difference between the apparent temperature of the earth as seen in space and the actual temperature of the earth s surface is attributed to the greenhouse effect. 

Radiation is the rate of heat transfer by electromagnetic waves emitted by matter. Unlike conduction and convection, radiation does not require an intervening medium to propagate. The basic rate of radiation heat-transfer equation between a high temperature (Th) black body and a low temperature Tf) black body is Stefan-Boltzmann s law ... 

All this is related to the distinction between chemical and physical properties. Physical properties describe what a body is, as it is now. Chemical properties describe what a body can become, how it can react with other identifiable bodies. When bodies mix physically their properties blend properties common to both may be intensified, others are more or less cancelled out or diluted, but the original properties are still there in the mix. Black and white paint can be mixed to any shade of grayness some shades might be distinctive enough to be given names, but there are no sharp boundaries. 

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