Final answer:
The rapidity at which a star burns its fuel is determined by its mass, luminosity, core pressure, and core temperature. More massive stars have higher core temperatures and burn fuel more rapidly, resulting in shorter lifespans despite having a greater amount of fuel.
Step-by-step explanation:
What determines how rapidly a star burns up its fuel? The primary factors include the mass of the star, luminosity, pressure in its core, and the temperature in its core. Essentially, all of these choices combined determine a star's rate of fuel consumption. A star's core temperature is critically dependent on its mass, with more massive stars having more weight in their overlying layers, which in turn requires higher pressure to balance. This high pressure is only achievable with a higher temperature, leading to a faster rate at which hydrogen is fused into helium.
Massive stars possess high core temperatures and pressures, and thus they have high luminosities. However, despite having more fuel, they burn through it much more quickly than their low-mass counterparts, resulting in significantly shorter lifespans. The relationship between a star's mass, luminosity, and lifetime can be expressed as T = 10¹⁰ (M/L), where T is the lifetime of the star, M is its mass, and L is its luminosity, both compared to the Sun's values.