Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2015 / S25 / 3 / 1 / Solution

Put $\vartheta =T-T_0$ and assume $C>0$, $\lambda >0$. The linear differential equation for a constant forcing step isMultiplying by the integrating factor $e^{\lambda t/C}$ and integrating from zero to $t$ givesThe response initially grows at rate $F_0/C$ and tends to the equilibrium warming $F_0/\lambda$. Heat capacity per unit area and radiative-feedback units make $k_T$ an inverse time.