Lord Kelvin estimated the age of the earth using the principles of thermodynamics. What range of ages did he come up with?

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When assessing Lord Kelvin’s estimate for the earth’s age using thermodynamics, we must compare each option to the historical reasoning Kelvin used and the numbers he produced.
Option 1: '1-60 million years' — This range is inconsistent with Kelvin’s typical ballpark, which tended to be on the younger side but not as low as 1 million and not as broad as 60 million given his calculations. He used thermal data and estimates of cooling from an initially very hot earth, leading to a narrower, older-labeled range rather than this wide, extremely low span.
Option 2: '100–150 million years' — This would place the earth much older than Kelvin’s estimates allowed. Kelvin’s calculations, grounded in cooling curves and assumptions about initial temperature and heat flow, yielded ages substantially less than 100 million years. Hence this option overshoots his upper bound.
Option 3: '500–1000 million years' — This corresponds to the conventional Darwinian/radiometric timescales that modern geology accepts, but Kelvin’s thermodynamic cooling model could not accommodate such an ancient age given the physics and inputs available in his era. It is too large to be consistent with his framework.
Option 4: '20–40 million years' — This is the range that aligns with Kelvin’s fundamental approach: applying cooling rate calculations to estimate how long the Earth would take to cool from an initial high temperature to its present state, using plausible initial conditions and conductivities. Within his model and data, a few tens of millions of years is the companion range he arrived at, making this the most consistent choice among the options.
Thus, each option is weighed against Kelvin’s thermodynamic cooling method and the plausible parameter choices, with Option 4 matching the historical outcome most closely while the others conflict with the cooling-based constraints or push beyond the limits of his method.

My LMS Subjects Quiz Topic 3: Formation of the solar system

Lord Kelvin estimated the age of the earth using the principles of thermodynamics. What range of ages did he come up with?

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