Suppose a star having twice the mass of the Sun is 10 times more powerful. How many years is its lifetime on the main sequence?
The main sequence of a star is defined as the time duration during which the star is converting hydrogen to helium. For example, our Sun will be in the main sequence for about 10 billion years ( `10^10` years). Stars obtain their energy by nuclear fusion, a reaction in which hydrogen is converted to helium, along with tremendous amount of energy. The amount of time a star will be on main sequence is dependent on its mass and its luminosity. More the mass, longer is the duration (for the same luminosity). Similarly, more luminosity, lesser will be the time spent on main sequence (for same mass).
In this case, the star has twice the mass as Sun and has 10 times the luminosity as Sun. That is, star has 2 times the mass and consumes the hydrogen at 10 times the rate of our Sun. Thus the ratio of time on main sequence is 2/10 = 1/5 or 20%. Thus, this star will only spend one-fifth the solar time on main sequence, which is equal to 2 billion years (= 10^10 / 5).
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