Lord Kelvin and the heat transfer problem

Lord Kelvin argued that life on Earth had to be younger than 100 millions years, the time it takes for heat from the center of the Earth to diffuse to its surface. For if the Earth’s surface had been cool enough for life for more than 100 millions years, its molten core would have long lost all its heat, and the Earth now would be too cold for volcanic activities. Lord Kelvin’s claim was later discredited by the discovery of radioactivity, but his treatment of the heat transfer problem is widely accepted as correct.

Diffusion of heat is essentially a Brownian motion, in which the distance traveled is proportional to the square root of time. If it takes 100 millions years for heat to travel the radius of the Earth, i.e., 6000 km, then it would take 100 years for heat to travel 6 km. Scaling down further, it would take 3000 seconds for heat to go 6 m, and only 0.3 seconds for 6 cm.

Then why do I have to cook an egg in boiling water for 6 minutes???

2 responses to “Lord Kelvin and the heat transfer problem

  1. My guess is that the proportionality constants (diffusion coefficients) are very different in two cases. But I could not find the numbers that support for the difference of about two orders of magnitude.

  2. As pointed out by John Perry in 1895 a variable conductivity in the Earth’s interior would expand the computed age of the Earth to billions of years, as later confirmed by radiometric dating. Contrary to the usual representation of Kelvin’s argument, the observed thermal gradient of the Earth’s crust would not be explained by the addition of radioactivity as a heat source, only a change in the conductivity of rock, as observed by modern geophysical studies.

    https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget

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