Volcanic Activity as a Function of Planetary Size

The level of volcanism on a planet plays a significant role in shaping the surface and its characteristics. The purpose of this paper is to obtain a theoretical framework that relates the extent of volcanism on a terrestrial planet to its size, i. e. , its radius. We use a simplified model of a planet which has been formed in a molten state and gradually cools to form a hard crust on the exterior. The underlying assumption in this model is that the molten liquid in the interior exists in hydrostatic equilibrium, and that there exists an isentropic temperature gradient. If we use the argument that volcanism is related to the hydrostatic pressure below the crust, basic mechanics and thermodynamics gives us the relation that we desire.