stellar evolution - Burning Out Stars

The easiest way to think of it is terms of the cube square law coming into play.

The speed at which a star can radiate heat is mostly dependent on its surface area. but it's ability to generate heat is dependent on its volume. Surface area increases with the square of the increase in radius but volume increases with cube of the radius. As a star grows in a diameter it's inside grows faster than its outside.

Even if all other factors stayed the same, the star would grow hotter because it has less surface area to radiate from.

Since gravity is dependent on volume, the gravitational compression (simplistically) scales with the cube as well. So, a larger star compresses its interior more per unit of mass than does a smaller star.

As Joan.bdm pointed out, stars have an interior volume, the burning zone down towards the core in which the pressures are high enough for fusion to take place. Probably should call it the burning volume

The burning volume is the volume in which fusion can occur. Fusion occurs once a specific threshold of heat and pressure have been reached. Below that threshold, fuel consumption is zero.

The cube square law means that the relative size of the burning volume to total volume increases faster than the diameter. E.g If a small star has ten percent of its mass inside the burning zone, a star with twice the diameter will have 20% of its total volume inside the burning zone. (actual ratios invented for demonstration purposes.)

A higher percentage of the larger star's total mass is inside the burning zone compared to a smaller star so a higher percentage of the star's mass is subject to fusion at any given time, so a higher percentage of the star's total "fuel" is being "burned" at any one time than in a smaller star.

The addition of more fusible isotopes also does not scale linearly. Fusing heavier elements does not release as much energy per unit of mass as lighter ones and they require higher temperatures to start i.e. heavier elements are a poorer fuel. The heavier elements are also produced by fusing lighter ones so the star has to burn fuel to make fuel. Since heavier elements require higher temperatures to fuse, the burning volume for them is smaller than that for lighter elements. Stars usually can't burn more than small percentage of the elements isotopes they produce so the notional increase in fuel supply doesn't compensate for the higher burn rate of lighter elements.

It's like the bard said, "The candle that burns twice as bright, burns half as long."