Question

The yellow star has much less mass than the blue star and so will live longer explain why.

Answer 1

     The radiation emission is closely connected with their visible color. In ascending order, the hottest are blue, yellow and red planets. The Stefan-Boltzmann's Law says that the radiation emitted by a hot body is given by:

$E=eA \alpha T^4$
 
     Where "A" is the area. Considering the planet as a sphere, we have to its area is givin by:

$A=4 \pi r^2$
 
     So we have that radiation is proportional to the radius of the planet. If the radius increases, the volume will increase. If a planet is larger, we can deduce that it has more mass.
     Therefore, the more radiation the planet emit, it will be hotter, soon have more mass.

If you notice any mistake in my english, please let me know, because i am not native.

Answer 2

The more mass a star has the shorter the lifespan.

The less mass a star has the longer the lifespan.

So, that means that the yellow star (the one with less mass) will live longer.

Also . . .

Blue Stars are hotter than Yellow Stars.

This means that the Blue Star will Burn out quicker than the Yellow Star.