Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2016 / S29 / 1 / 4 / b / Solution

Jupiter emits at about 130 K rather than the solar-only estimate around 111 K. Intrinsic heat contributes additional outgoing flux, so $\sigma T_{\mathrm{emit}}^4=F_{\mathrm{absorbed}}+F_{\mathrm{internal}}$. The difference of fourth powers is the relevant energy excess, not their direct temperature difference. Cooling and contraction of the interior provide the main physical motivation for including this extra term.