Why does the Sun look yellow when its light is white?

1it's white

Sunlight is a blend of every visible color. A glass prism pulls them apart into a rainbow, and the same colors recombine to make white. Seen from space, with no air in the way, the Sun is a brilliant white disc.

So the question has a catch: the Sun's light is white, and it is our atmosphere that makes it look yellow.

Sunlight is white: every color mixed together.

2air bounces blue

Air is made of molecules far smaller than the wavelength of light. They scatter light, and short wavelengths scatter much more strongly: roughly in proportion to one over the wavelength to the fourth power. Blue light near 450 nanometres scatters about four times more than red light near 650.

So as sunlight crosses air, some blue is knocked out of the beam in all directions. The light that keeps going straight toward your eye has lost some blue, so it looks yellower.

Air scatters blue light far more than red, so the direct beam loses its blue.

3noon: thin air

At midday the Sun is high and its light goes almost straight down through the atmosphere, the shortest possible trip. Little blue is removed, so the Sun looks white with a faint yellow tinge. Even then, never look straight at it.

High Sun, short path, little blue lost: pale yellow-white.

4sunset: thick air

When the Sun sits near the horizon, its light has to cross a long, slanting path through the lower atmosphere, roughly forty times as much air as straight overhead. The blue is almost entirely scattered out and then even the green fades, so the light that reaches you is orange or red.

Low Sun, long path, almost all blue lost: orange and red.

5the blue sky

That lost blue isn't wasted. Scattered across the sky, it is the blue you see overhead. The same bouncing makes blue skies and red sunsets.

6the whole idea

So the whole story: white light goes in, air scatters out the blue, and the more air it crosses, the redder the Sun looks.