Kelvinor

Kelvinor raises his thermometer sword over an Earth far older than he thinks.

The Physics

In 1862 William Thomson, later Lord Kelvin, treated the Earth as a body that began molten and has cooled by conduction alone. From the measured rise of temperature with depth, a starting temperature and the rock's diffusivity, the half-space conduction solution gives an age. He bracketed it between 20 and 400 million years.

The model left out heat carried by convection inside the Earth (John Perry argued in 1895 that a more conductive interior gives far larger ages) and radioactive heating, discovered after 1896. In 1956 Clair Patterson, using lead isotopes in meteorites, found 4.55 ± 0.07 billion years.

t ≈ T₀² / (π κ G²)

• t: age (s)
• T₀: starting temperature (K)
• κ: rock thermal diffusivity (m²/s)
• G: surface temperature gradient (K/m)

Thomson, “On the secular cooling of the earth”, Trans. R. Soc. Edinb. 23, 157 (read 1862); Perry, Nature 51, 224 (1895); Patterson, Geochim. Cosmochim. Acta 10, 230 (1956).

Honest caveat: Radioactivity alone did not fix the estimate; convection mattered at least as much. His conduction mathematics was sound; the model was missing pieces.

On the shirt

Front: Kelvinor, the pixel-art character, with “FAR TOO YOUNG”. Back: the conduction-only age formula, Kelvin's 1862 range, the missing convection and radioactive heat, and Patterson's 1956 age. Printed on a unisex tee.