In this problem, we\'re going get a rough estimate the amount of uranium fuel it

Question

In this problem, we're going get a rough estimate the amount of uranium fuel it would take if the US recieved 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% to 35%.

Lets assume we have a 1000 MWe electrical power plant that recieves its thermal energy from pressured water nuclear reactor (PWR) and has overall thermal efficiency of 30%.

a) What is the total thermal power generated by the reactor?
Pthermal = MW *
3333.33 OK




b) Lets assume that all fission events are

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





c) What is the mass of 235U fissioned in one year?
Use = kg
569.4 NO





d) 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 2.7% of the fuel is actually 235U by mass. What is the total mass of fuel is used in one year?
Usetotal = kg
569.4 NO



e) 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 = m3




f) Take the electrical production of the US to be around 2.5X1012kWh/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 = m3






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










Closing Thoughts: Your answers to parts (e) through (g) are good rough estimates, but to be more precise, we would need to include several significant factors. First, the fuel pellets are not all U but are normally in the form of UO2 which has a different density than that of pure U. Also, we have not included the fact that after fissioning the small amount of 235U actually turns into daughter products which have a different density nor have we included any thermal expansion. Still, it gives us a feeling for sizes. compare this amount of fuel "used" to the amount of fuel used in a coal powered electrical generation plant. Is one much greater than the other? Could the country store this much material annually on a semi-permanent basis?
You may want to use the following table of atomic masses:










Table of masses
141Ba 140.914406 u 144Ba 143.92294 u 139Te 138.93473 u
141Cs 140.91963 u 90Kr 90.9234424 u 91Kr 89.9195238 u
92Kr 91.9261528 u 94Zr 93.9063158 u 93Rb 92.92157 u
235U 235.04392 u p 1.00728 u n 1.00867 u

Explanation / Answer

(a) average efficiency=0.3

Thermal power= electric power/ eficiency= P= 1000/0.3=3333.33 MW

(b) average energy released per fission= 200 MV

fission rate= 3333.33/(200x1.6x10-19)=1.04x1020 fission /sec

(c) m= N ma t/Na

t =1 year=31536000 seconds

m=1.04x1020 *235*31536000/(6.022x1023)=1279873 grams

m=1279.8 Kg

(d) Total mass= m/0.03= 1279.8/0.03

Total mass=42662 kg

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