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

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 $d(C-C_1)/dt=-2k(C-C_1)$. ThusThe atmospheric burden falls from one to one half with time constant $(2k{)}^{-1}$, 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.