(Abridged) The thermal history of the intracluster medium (ICM) is complex. Heat input from cluster mergers, AGN, and galaxy winds offsets and may even halt the cooling of the ICM. Consequently, the processes that set the properties of the ICM play a key role in determining how galaxies form. In this paper we focus on the shock heating of the ICM during cluster mergers, with the eventual aim of incorporating this mechanism into semi-analytic models of galaxy formation. We use a suite of hydrodynamic simulations to track the evolution of the ICM in idealised two-body mergers. We find the heating of the ICM can be understood relatively simply by considering the evolution of the gas entropy during the mergers. We examine the processes that generate the entropy in order to understand why previous analytic shock heating models failed. We find that: (1) The energy that is thermalised in the collision greatly exceeds the kinetic energy available when the systems first touch. The smaller system penetrates deep into the potential well before it is disrupted. (2) For unequal mass mergers, most of the energy is thermalised in the more massive component. The heating of the smaller system is minor and its gas sinks to the centre of the final system. (3) The bulk of the entropy generation occurs in two distinct episodes. The first episode occurs following core collision, when a shock wave is generated that propagates outwards from the centre. This causes the combined system to expand rapidly and overshoot hydrostatic equilibrium. The second episode occurs as this material is shock heated as it re-collapses. This revised model for entropy generation significantly improves our physical understanding of cosmological gas simulations.
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