Solution (source code)

= Solution

For the historical laboratory context, intense heating could be obtained from an electric arc between carbon electrodes and from an oxyhydrogen flame. The first converts electrical <work> into a very hot emitting region; the second releases <chemical energy> rapidly in <combustion>. An intense light or an ability to melt a particular solid establishes a useful physical effect, but does not by itself provide a calibrated numerical <temperature>.

The cold end could be reached by rapidly evaporating a volatile material and reducing the surrounding <pressure>. In <Faraday's carbon-dioxide and ether cooling experiment>, a bath of solid <carbon dioxide> and <diethyl ether> was placed under an air-pump receiver. Removing vapour promoted further cooling. Faraday's 1845 report gives an alcohol-thermometer reading near $-106\,{}^\circ\mathrm F$ in the atmospheric-pressure bath and $-166\,{}^\circ\mathrm F$, approximately $-110\,{}^\circ\mathrm C$, under reduced pressure. He explicitly noted thermometer lag, thickening alcohol and possible errors of several Fahrenheit degrees. These are dated reported estimates, not a claim to a modern cold-temperature record.<On the Liquefaction and Solidification of Bodies Generally Existing as Gases by Michael Faraday>[1845, printed p. 158: reduced-pressure bath, alcohol-thermometer graduation and uncertainty]{ref}

Measurement must be separated from temperature production. A liquid-in-glass thermometer works only while its liquid, glass and graduation remain usable. A <gas thermometer> infers <temperature> from reproducible gas pressure or volume changes, with calibration and departures from ideal-gas behaviour accounted for. At high temperatures, suitable expansion or calorimetric <pyrometers> can be compared against known points, but material changes and extrapolation introduce error. For example, transferring a hot body of known thermal properties into a <calorimeter> estimates its starting <temperature> only after allowing for its heat capacity and heat lost in transfer. The very hottest arc regions are not safely assigned the reading of an ordinary mercury thermometer.

Faraday's published lectures demonstrate the carbon-electrode electric light and electrical heating of platinum. They provide contemporary apparatus context; the later reprint's date is distinguished in its bibliography entry.<On the Various Forces of Nature by Michael Faraday>[Lecture VI, carbon points and the heated platinum bridge]{ref}