Final answer:
The lifespan of a main-sequence star is closely related to its temperature and mass; higher temperatures and larger masses result in shorter lifespans due to faster fuel consumption.
Step-by-step explanation:
The lifespan of a main-sequence star is indeed a function of its temperature, as well as other factors. It turns out that the higher the temperature of a main-sequence star, which is also related to its mass, the shorter its lifespan. This is because massive stars have higher temperatures as well as higher luminosities, which leads them to burn through their fuel much more quickly than stars with less mass and lower luminosity.
The relationship between a star's mass (M), its luminosity (L), and its lifespan (T) can be expressed by the equation T = 1010 y (M/L). Accordingly, main-sequence stars with lower temperatures, which also tend to have smaller masses, correlate with longer lifespans. Simply put, a larger mass leads to a more substantial gravitational pull, increasing the rate of fusion and thus the luminosity, speeding up the consumption of nuclear fuel and shortening the star's lifespan.
To give an example, a star with the mass of the Sun (1 solar mass) has an estimated main-sequence lifespan of approximately 10 billion years, while a star with 0.4 solar mass may last around 200 billion years on the main sequence. This contrast vividly illustrates how mass and temperature influence stellar lifetimes.