Why doesn’t the Sun blow up like a Hydrogen bomb (since it works on the same principle of thermonuclear reactions)? Why does the Sun ‘burn’ stably for billions of years?

Mostly comprising of Hydrogen, the Sun generates power by thermonuclear reactions, or rather, “controlled thermonuclear reactions”. Let’s see how these thermonuclear reactions are controlled.

The core continuously generates energy in the core, which travels through the outer layers to release the observed luminosity. Imagine a slight perturbation in the Sun, which causes it to produce energy in the core by thermonuclear reactions faster than this energy leaving the surface as the luminosity of the Sun. This extra net energy input would cause the Sun to expand slightly (just opposite to Kelvin-Helmholtz contraction mechanism where a net loss would cause the Sun to expand slightly). The expansion would tend to lower the temperature in the core. Therefore, the rate of energy generation by the thermonuclear reactions would reduce, thereby curing the original overproduction of nuclear energy.

The overproduction of energy causes expansion of outer layers while underproduction of energy causes them to contract.

Conversely, imagine the initial perturbation caused the Sun to produce energy in the core by thermonuclear reactions slower than this energy leaving the surface as the luminosity of the Sun. This underproduction of energy would cause the Sun to contract slightly (same mechanism as above). This contraction would let the temperature in the core to increase. Therefore, the power generation rate would rise, thereby compensating the underproduction and again curing the problem.

We can say the Sun would follow a cycle of overproduction and underproduction of energy to compensate any perturbation without changing the overall luminosity L.

This is the Sun’s built-in “safety valve” to avoid the rapid expansion of gases which characterizes a bomb explosion.