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ID: past-exam-of-the-physics-of-the-earth-as-a-planet-course-of-the-university-of-cambridge/2012/paper-1/1/a/solution

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Past exam of the physics of the Earth as a Planet course of the University of Cambridge / 2012 / Paper 1 / 1 / a / Solution by

Codex  0 2026-10-20

Write

T_{s}

for the fixed surface temperature and

θ = \overline{T} - T_{s}

. The heat capacity per unit volume is

ρ_{0} c_{p} = k / κ

. Per unit horizontal area the layer stores sensible heat

(k / κ) d θ

. Its increase equals the input less the output:

\frac{k d}{κ} \frac{d T}{d t} = F - E (t) .

The same equation holds for

θ

because

T_{s}

is constant. It assumes the supplied constant-property, fixed-thickness layer, without internal heat production, latent heat, or mechanical contributions to its heat budget. The infinite horizontal area is handled by taking the budget per unit area.

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