Narration script

Unit five, blackbody radiation. Every object glows, with a spectrum that depends on its temperature. An ideal absorber and emitter, called a blackbody, follows Planck's law exactly. The Sun is close to a fifty-seven hundred kelvin blackbody, which is why sunlight peaks in the visible. A lamp filament is about three thousand kelvin, which is why it puts out mostly infrared. And a solar cell at room temperature is itself a very faint infrared emitter, a fact that sets its ultimate efficiency limit.

By the end you should be able to describe Planck's law in words, use Wien's law to find a peak wavelength, use the Stefan-Boltzmann law for total emitted power, and explain why the Sun is only approximately a blackbody, and why ordinary lamps are poor stand-ins for sunlight.

This physics shows up all over solar manufacturing: in the solar spectrum itself, in the efficiency limit, in infrared cameras that inspect modules, and in the pyrometers that control crystal-growth and firing furnaces.

A blackbody absorbs all light that hits it, at every wavelength. Kirchhoff's law says that a good absorber at some wavelength is an equally good emitter at that wavelength. So a blackbody emits the most thermal radiation possible for its temperature. Real objects have an emissivity, a number between zero and one, that scales the ideal down.

Planck's law gives the shape of the spectrum. You do not need to memorise the formula, but understand its story. At short wavelengths, each photon costs too much energy compared with the available thermal energy, so emission is suppressed exponentially. At long wavelengths, emission tails off too. In between is a peak, and both its position and height depend only on temperature.

Here are four Planck curves on a logarithmic scale: the Sun at fifty-seven seventy-two kelvin, forty-five hundred, a halogen lamp at thirty-two hundred, and a household incandescent bulb at twenty-seven hundred. Two things to notice. Hotter bodies are brighter at every single wavelength; the curves never cross. And hotter bodies peak further to the left, at shorter wavelengths. The dots mark the peaks, and the yellow band marks the visible. Only the Sun's peak falls inside it.

That peak shift is Wien's displacement law: peak wavelength equals a constant, about two point nine millimetre-kelvins, divided by temperature.

Run the numbers. The Sun peaks near five hundred and two nanometres, green-blue. A halogen filament at thirty-two hundred kelvin peaks near nine hundred and six nanometres, already in the infrared. A household bulb, near one thousand and seventy. And a solar module at room temperature peaks near ten micrometres, deep in the thermal infrared. That is exactly what a thermal camera sees.

Add up the whole curve and you get the Stefan-Boltzmann law. Total emitted power per area equals emissivity, times a constant sigma, times temperature to the fourth power. Fourth power is steep: double the temperature, and you get sixteen times the power.

Every square metre of the Sun's surface radiates about sixty-three megawatts. A module at sixty degrees Celsius, with an emissivity around zero point eight five, which is an estimate, emits about five hundred and ninety watts per square metre from each face. It also absorbs infrared from the sky and ground, so the net cooling is smaller, but radiation and convection together are how the module sheds the heat we calculated in unit two.

The Sun's effective temperature is fifty-seven seventy-two kelvin, the internationally agreed nominal value. It is defined as the temperature of a blackbody of the same size that radiates the same total power.

This figure compares measured sunlight above the atmosphere, in colour, with a fifty-seven seventy-two kelvin blackbody, as the smooth line. The overall shape matches well. But the real Sun is short in the ultraviolet and blue, with many dips called Fraunhofer lines, and slightly long in the infrared. That is because the light comes from layers at different depths and temperatures, and cooler upper layers absorb specific wavelengths. For engineering we always use the measured spectrum. The blackbody is for understanding and for theoretical limits.

Now lamps. A tungsten filament at twenty-seven hundred to thirty-two hundred kelvin puts most of its output into the infrared. Too little blue, too much infrared, so a halogen lamp is a poor imitation of sunlight. Professional solar simulators use xenon arc lamps or filtered LED arrays and are graded for spectral match.

In Lab C you will estimate a filament's temperature from its electrical resistance, because tungsten's resistance rises with temperature. In this example, a bulb measures two ohms cold and twenty-eight ohms hot, a ratio of fourteen. Using an approximate fit to tabulated data, that corresponds to about twenty-seven hundred kelvin, peaking near one point oh seven micrometres. The fit is an estimate, good to about ten percent.

Finally, the cell itself. A solar cell at room temperature emits a little thermal radiation. And a cell under forward voltage emits extra light near its band gap; that is electroluminescence, which factories use to image cells. Shockley and Queisser realised that whatever can absorb light must also emit it. That emission sets the minimum dark current of a perfect cell, and it is the heart of the efficiency limit in unit eleven.

Misconceptions. Black does not mean emits nothing; black objects are the best emitters. The Sun is not yellow; it is essentially white and looks yellow through the atmosphere. A halogen lamp is not a good test light for solar cells. And not only hot things radiate; everything above absolute zero does.

In the factory, pyrometers and infrared cameras measure temperature in crystal pullers, firing furnaces and module inspection. Simulator lamps are graded by spectral class. And electroluminescence imaging, a standard inspection, exists because absorption and emission are linked.

Do the review questions, including a Wien and a Stefan-Boltzmann calculation. Next unit, we follow sunlight from the Sun's surface to the top of Earth's atmosphere, and derive the solar constant.