# Reactor fuel and waste: fission/fusion problem

1. May 4, 2014

### tri5

1. The problem statement, all variables and given/known data

In this problem, we're going get a rough estimate the amount of uranium fuel it would take if the US received all its electrical power from nuclear power plants.

The size of a power plant in normally given as the about of electrical power it can produce when running a full capacity. This electrical power produced can be very different than the mechanical or thermal power that was required to produce this electricity. For example, power plant might have a \"thermal efficiency\" of 25\% and so require 100 MWt (mega-watts of thermal power) to produce 25MWe (megawatts of electrical power). The efficiency will vary from plant to plant but an approximate range is from around 2\5% to 35\%.

Lets assume we have a 103 MWe electrical power plant that receives its thermal energy from pressured water nuclear reactor (PWR) and has overall thermal efficiency of 30\%.

You may want to use the following table of atomic masses:

Table of masses
141Ba 140.9144 u 144Ba 143.9229 u 139Te 138.9347 u
141Cs 140.9196 u 90Kr 89.91952 u 91Kr 90.92344 u
92Kr 91.92615 u 94Zr 93.90632 u 93Rb 92.92157 u
235U 235.0439 u p 1.00728 u n 1.00867 u

I posted an image of the problem along with the table of masses as an attachment.

1) What is the total thermal power generated by the reactor?
Pthermal = 3333.33 MW

2) Lets assume that all fission events are
There is supposed to be reaction equation here.
I posted a picture of the reaction at the bottom.

What is the rate of fission events in the reactor core?
Rfission = 1.16e20/sec

3) What is the mass of 235U fissioned in one year?
Use = 1428.73105 kg

4) A key point here is that not all of the uranium fuel in the reactor is 235U. Most of it is actually a different isotope, 238U, which does not fission in standard reactors. Lets assume the fuel is \"enriched\" so that 2.8\% of the fuel is actually 235U by mass. What is the total mass of fuel is used in one year?
Usetotal = 1428.7310/.028 kg

5) Assume that all the fuel used in one year must actually be removed as high level radioactive waste. What volume of waste must be removed from the reactor annually and placed in long term storage?
Vtotal = 2.68558 m^3
Help: Recall that the density of the uranium can be estimated at 19,000 kg/m3.

6) Take the electrical production of the US to be around 2.5X10^12 kWh/year. If all of the electrical power was generated by nuclear power plants similar to the one described above, what would the amount of waste that would need to be stored annually?
Vnational = m^3

7) If this waste were formed into a cube, what would be the length of the cube's sides?
L =

2. Relevant equations

I posted an equation sheet below.

3. The attempt at a solution
I'm having trouble with number 6.
I converted 2.5x10^12 kWh/yr to J/s. Then divided by the answer given in number 1. That number was then multiplied by the answer in number 6.
The thinking behind this was that since one reaction produces the volume in question number 5, than a multiple of that volume would would produce an amount of waste given an amount of power output. I posted the written work below.

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2. May 4, 2014

### SteamKing

Staff Emeritus
It's not shown in your calculations how a plant producing 103 MWe of power at 30% thermal efficiency requires a thermal input of 3333.33 MW.

Also, you shouldn't write percentages like 30\%. The '\' is apparently the result of some weird formatting with the problem statement.

3. May 4, 2014

### dauto

You shouldn't divide 2.5x10^12 kWh/yr to J/s by the answer 1. Instead, divide it by the 103 MW actual electric power produced. By the way, the answer 1 is a bit off.