Respuesta :
Answer:
1) Mass that needs to be converted at 100% efficiency is 0.3504 kg
2) Mass that needs to be converted at 30% efficiency is 1.168 kg
Explanation:
By the principle of mass energy equivalence we have
[tex]E=mc^{2}[/tex]
where,
'E' is the energy produced
'm' is the mass consumed
'c' is the velocity of light in free space
Now the energy produced by the reactor in 1 year equals
[tex]Energy=Power\times time\\\\\therefore Energy=1\times 10^{9}\times 365\times 24\times 3600\\\\Energy=31.536\times 10^{15}Joules[/tex]
Thus the mass that is covertred at 100% efficiency is
[tex]mass=\frac{Energy}{c^{2}}\\\\mass=\frac{31.536\times 10^{15}}{(3\times 10^{8})^{2}}\\\\mass=\frac{31.536\times 10^{15}}{9\times 10^{16}}\\\\\therefore mass=0.3504kg[/tex]
Part 2)
At 30% efficiency the mass converted equals
[tex]mass|_{30}=\frac{mass|_{100}}{0.3}\\\\mass|_{30}=\frac{0.3504}{0.3}\\\\mass|_{30}=1.168kg[/tex]
