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 / 2 / a / Solution

Temperature is continuous through an instantaneous carbon injection. With $T(0)=0$ and $C(0^{+})=1$, $\boxed{\dot{T}(0^{+})=b_0}$. Its initial slope is finite; the emission pulse makes the carbon burden jump but does not give this first-order thermal model an instantaneous temperature jump.