ABSTRACT When comets approach the Sun, their surface is heated and the volatile species start to sublimate. Due to the increasing gas pressure, dust is ejected off the surface, which can be observed as cometary coma, dust tail, and trail. However, the underlying physical processes are not fully understood. Using state-of-the-art results for the transport of heat and gas as well as of the mechanical properties of cometary matter, we intend to describe the activity pattern of comets when they approach the Sun. We developed a novel thermophysical model to simulate the dust ejection from comet 67/Churyumov–Gerasimenko’s south-pole region at perihelion. Based on the input parameters, this model computes the sub-surface temperature profile, the pressure build-up, and the redistribution of volatiles inside the cometary sub-surface region and provides mass-loss rates of dust and gas as well as typical sizes and ice content of the ejected dust chunks. Our thermophysical model allows for continuous gas and dust ejection from the Southern hemisphere of comet 67/Churyumov–Gerasimenko at perihelion. We find that the model output is in general agreement with the observed Rosetta data. The sublimation of CO2 ice drives the ejection of very large ($\gtrsim 10\, \mathrm{cm}$) chunks, which contain $10\, {{\ \rm per\ cent}}$ to $90 \, {{\ \rm per\ cent}}$ of the initial water–ice content. In contrast, the outgassing of H2O ice causes the lift-off of small clusters of dust aggregates, which contain no ice.