Calculating Uranium-235 Usage in Nuclear Power Plants

[rose1]

Homework Statement

Given that the average fission produces 200 MeV in energy, and that nuclear plants have an efficiency of 33%, how many fissions take place each second in a plant producing 1000 MW of electricity? How much uranium-235 is being used per day?

The Attempt at a Solution

I've solved the first part: 200 MeV of energy = 3.2 x 10^-11 watt-seconds. From this, 3.1 x 10^10 fissions per second produce 1 W of thermal power. For 330 MW, that equals 1.029 x 10^19 fissions per second. ...But I don't know how to go about finding how much uranium-235 is used per day. I know that U-235 only makes up 4% of a typical LWR, but I'm in the dark as to how much U-235 each fission would consume... Maybe I'm just having an off-day, and the answer's extremely easy...

 

[Astronuc]

Well, the fission energy ultimately becomes thermal energy, and that's one of the keys in solving the problem.

Firstly, one must recognize that the thermal energy is converted into electrical energy with an efficiency of 33% or 0.333. So MWe = 0.333 * MWt. Remember W is power.

So one must determine the MW-h or MJ of thermal energy in one day.

Then given the number of J per reaction one can determine the number of U-235 nuclei.

From that one determines the mass of U-235.

 

[rose1]

Thank you very much!