Final answer:
The heat transfer from the hot rock to the sides of the vacuum chamber is primarily due to radiation, as conduction and convection require a material medium to occur, which is absent in a vacuum.
Step-by-step explanation:
The primary mode of energy transfer in the process described, where a hot rock is placed on an insulating stand inside a small vacuum chamber and the air is removed, is most accurately described by radiation. This is because radiation is the transfer of energy in the form of electromagnetic waves and does not require a medium, such as air, to occur. Both conduction and convection require a material medium for the transfer of heat. Conduction relies on direct physical contact between materials, and convection involves the movement of a fluid, such as air or water, to transfer heat. In a vacuum, conduction and convection cannot occur, leaving radiation as the primary mechanism by which the rock's heat is transferred to the sides of the container.