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Summary

Added notes

The radial lines denote key temperatures, clockwise from bottom including He evaporation (dotted cyan) around 4K ↔ 3265GB/nJ (just CCW from the 4732.51GB/nJ of the 2.76K cosmic background) and N₂ evaporation (dashed cyan) around 77K ↔ 170GB/nJ, CO₂ sublimation around -78.5^oC ↔ 67.1GB/nJ (solid cyan), H₂O liquification around 0^oC ↔ 47.8GB/nJ and evaporation around 100^oC ↔ 35.0GB/nJ (dashed-green), "red-hot" (solid red) around 500^oC ↔ 16.9GB/nJ, rock melting around 1500^oC ↔ 7.37GB/nJ (solid magenta), graphite sublimation (dashed magenta) around 3642^oC ↔ 3.34GB/nJ, and the surface of the sun (dotted magenta) around 5778K ↔ 2.26GB/nJ ≈ 2.01 nat/eV. The dashed red lines represent the min-max European temperature range (from 0^oF ↔ 51.2GB/nJ to 100^oF ↔ 42.0GB/nJ) on which Fahrenheit based his scale, at top of which is also the human basal temperature at around 98.6^oF ↔ 42.1GB/nJ. Room temperature (3 o'clock) is defined as either 20^o = 68^oF ↔ 44.6GB/nJ ≈ 39.6 nat/eV = 1/kT or 22^oC = 71.6^oF ↔ 44.3GB/nJ ≈ 39.3 nat/eV = 1/kT, and therefore kT_room is about 1/40 of an electron Volt.

Inverted-population states for finite-energy systems are found on the left half of this plot. These include: (i) 1024 end-on dominoes acting like stonehenge in the earth's gravitational-field (grey-dotted) at -.001[J]/(k_Bln[1024]) ≈ -1.04×10¹⁹K ↔ -1.25×10^-15GB/nJ, (ii) a mole of excited Ne atoms in a He-Ne LASER ready for stimulated-emission (grey-dashed) at -1.96[eV]/(k_Bln[6×10²³]) ≈ -415K ↔ -31.5GB/nJ, and (iii) the orientation-temperature for 500,001 up out of 1,000,000 proton-spins in a 1 Tesla field (grey) at 1.41×10^-26J/(k_B(ψ[1+1000000-500001]-ψ[1+500001])) ≈ -1.41×10^-26J/(k_Bln[1000000/500001-1]) ≈ -255K ↔ -51.1GB/nJ where ψ[x] is the PolyGamma function. The dot-dashed grey lines are for 500,002 and 500,003 out of 1,000,000 protons oriented spin-up in that same 1[Tesla] field.

This plot illustrates that you can use either temperature T or reciprocal-temperature 1/kT to predict the direction of heat-flow. When you use temperature, remember that the highest possible temperature T is minus-zero-Kelvin and the lowest possible T is plus-zero-Kelvin. With coldness 1/kT, the lowest value is minus-infinity and the highest is plus-infinity so that heat energy naturally and simply flows from numerically low to numerically high 1/kT.

In the table of conversions above, note that the uncertainty-slope or coldness β≡1/kT in [GiB/nJ] or [GB/nJ] is nearly equal to the reciprocal of kT in [eV/nat]. Even more curiously, if we don't mind using binary-multiples i.e. gibiBytes instead of powers of ten, we can say that 1[nat/eV] = 1.04827[GiB/nJ] = 1.12557[GB/nJ]. Hence room temperature coldness is about 40[GiB/nJ] simply because kT at room temperature is about ¹/₄₀[eV].

Footnotes

1. ↑ Claude Garrod (1995) Statistical Mechanics and Thermodynamics (Oxford U. Press).
2. ↑ J. Meixner (1975) "Coldness and Temperature", Archive for Rational Mechanics and Analysis 57:3, 281-290 abstract.
3. ↑ Ingo Mueller (1972) Entropy, Absolute Temperature and Coldness in Thermodynamics: Boundary conditions in porous materials (Springer-Verlag, Wein GMBH) preview
4. ↑ Ingo Müller (1971) "The coldness, a universal function in thermoelastic bodies", Archive for Rational Mechanics and Analysis 41:5, 319-332 abstract.
5. ↑ Müller, I. (1971) "Die Kältefunktion, eine universelle Funktion in der Thermodynamik wärmeleitender Flüssigkeiten.", Arch. Rational Mech. Anal. 40, 1–36.
6. ↑ Day, W.A. and Gurtin, Morton E. (1969) "On the symmetry of the conductivity tensor and other restrictions in the nonlinear theory of heat conduction", Archive for Rational Mechanics and Analysis 33:1, 26-32 (Springer-Verlag) abstract.
7. ↑ J. Castle, W. Emmenish, R. Henkes, R. Miller, and J. Rayne (1965) Science by Degrees: Temperature from Zero to Zero (Westinghouse Search Book Series, Walker and Company, New York).
8. ↑ P. Fraundorf (2003) "Heat capacity in bits", Amer. J. Phys. 71:11, 1142-1151.

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