How is a star's luminosity related to its temperature and size?

A star's luminosity is directly related to its temperature and size.

The luminosity of a star is the total amount of energy it emits per unit time, and is measured in watts. The temperature of a star is related to the amount of energy it emits, with hotter stars emitting more energy than cooler stars. This is because the energy emitted by a star is proportional to the fourth power of its temperature, according to the Stefan-Boltzmann law.

The size of a star also plays a role in its luminosity, as larger stars have a greater surface area from which to emit energy. This means that larger stars are generally more luminous than smaller stars of the same temperature. However, there are exceptions to this rule, as some smaller stars can be more luminous than larger stars due to their higher temperatures.

The relationship between a star's luminosity, temperature and size is described by the Hertzsprung-Russell diagram. This diagram plots the luminosity of stars against their temperature, and shows that stars follow a distinct pattern based on their size and stage of evolution. By analysing the position of a star on the Hertzsprung-Russell diagram, astronomers can gain insights into its properties and evolution.