[UPSC IFoS 2010] Nuclear Physics (Q147, 10M)

A star converts all its hydrogen into helium, achieving 100\% helium. It then converts the helium into carbon via the reaction ^4_2\text{He} + ^4_2\text{He} + ^4_2\text{He} \xrightarrow{\quad} ^{12}_6\text{C} + 7.27\text{ MeV} The mass of the star is 5.0 \times 10^{32}\text{ kg} and it generates energy at the rate of 5 \times 10^{30}\text{ W}. How long will it take to convert all helium to carbon at this rate ?