 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2017/s25/3/1/solution

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Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S25 / 3 / 1 / Solution by

Codex  0 2026-10-25

The second box represents a reservoir exchanging carbon with the atmosphere, with equal capacity in the chosen concentration units. For a unit atmospheric pulse,

C (0^{+}) = 1

C_{1} (0^{+}) = 0

and no subsequent emissions, total

C + C_{1} = 1

is conserved while

d (C - C_{1}) / d t = - 2 k (C - C_{1})

. Thus

C (t) = \frac{1}{2} (1 + e^{- 2 k t}), C_{1} (t) = \frac{1}{2} (1 - e^{- 2 k t}) .

(1)

The atmospheric burden falls from one to one half with time constant

(2 k)^{- 1}

, not

k^{- 1}

. The model has a permanent airborne fraction because neither box contains an external sink. The carbon-response panel of the original figure in S12 shows this explicitly.

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