What happens when the sun becomes a Black Dwarf? When will this take place in the future?

This intricate process starts when the Sun burns through all of the hydrogen in its core, which will happen in around 5 billion years. As the nuclear fusion reaction fails, the core collapses due to the force of gravity of the Sun, and eventually it gets hot and dense enough to fuse helium, primarily forming carbon and oxygen.

The reaction's energy explosion pushes the gas' outer layers outward, causing them to cool and diffuse enough to glow red rather than white, turning the Sun into a red giant that will eventually swallow Earth (which would have long since gone extinct anyhow).

The outer gases eventually drift away, leaving behind the collapsed core, known as a white dwarf, which is so dense that a cubic centimeter would contain tons, not grams, of mass. This white dwarf core is left to run out of fuel permanently and cool down, eventually turning black, a process that could take a trillion years due to the white dwarf's small surface area and density.

Assuming current understanding of stellar evolution, the Sun will become a black dwarf after it has used up all of its nuclear fuel and cooled to the point where it emits no significant heat or light, which will happen in about 10^15 (1 quadrillion) years.