Question

In the nuclear fission process mass is converted into energy. Determine the total mass that must be converted to energy in one year by a 1 Giga-Watt nuclear if we a. assume 100% efficiency. b, assume only 30 % efficiency (nuclear energy to electrical energy conversion).

Answer 1

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

Step-by-step explanation:

By the principle of mass energy equivalence we have

`E=mc^(2)`

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

`Energy=Power* time\\\\\therefore Energy=1* 10^(9)* 365* 24* 3600\\\\Energy=31.536* 10^(15)Joules`

Thus the mass that is covertred at 100% efficiency is

`mass=(Energy)/(c^(2))\\\\mass=(31.536* 10^(15))/((3* 10^(8))^(2))\\\\mass=(31.536* 10^(15))/(9* 10^(16))\\\\\therefore mass=0.3504kg`

Part 2)

At 30% efficiency the mass converted equals

`mass|_(30)=(mass|_(100))/(0.3)\\\\mass|_(30)=(0.3504)/(0.3)\\\\mass|_(30)=1.168kg`