Question

Consider a nuclear power plant that produces 1200 MW of power and has a conversion efficiency of 34 percent (that is, for each unit of fuel energy used, the plant produces 0.34 units of electrical energy. Assuming continuous operation, determine the amount of nuclear fuel consumed by the plant per year.

Answer 1

The amount of nuclear fuel required is 1.24 kg.

Explanation:

From the principle of mass energy equivalence we know that energy generated by mass 'm' in an nuclear plant is

`E=m\cdot c^2`

where

'c' is the speed of light in free space

Since the power plant operates at 1200 MW thus the total energy produced in 1 year equals

`E=1200* 10^6* 3600* 24* 365=3.8* 10^(16)Joules`

Thus using the energy produced in the energy equivalence we get

`3.8* 10^(16)=mass* (3* 10^(8))^2\\\\\therefore mass=(3.8* 10^(16))/(9* 10^(16))=0.422kg`

Now since the efficiency of conversion is 34% thus the fuel required equals

`mass_(required)=(0.422)/(0.34)=1.24kg`