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 103 MWe electrical power plant that recieves 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 1) What is the total thermal power generated by the reactor? Pthermal = 3333.33 MW 2) Lets assume that all fission events are 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 = ??? 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 3% of the fuel is actually 235U by mass. What is the total mass of fuel is used in one year? Usetotal = ??? 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 = ??? m3   6) 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 7) If this waste were formed into a cube, what would be the length of the cube's sides? L = ??? m

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 103 MWe electrical power plant that recieves 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:

1) What is the total thermal power generated by the reactor?

Pthermal = 3333.33 MW

2) Lets assume that all fission events are

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 = ??? 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 3% of the fuel is actually 235U by mass. What is the total mass of fuel is used in one year?

Usetotal = ??? 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 = ??? m3  

6) 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

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

L = ??? m

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

Explanation / Answer

Ans 1

The generated electrical power is 103 MWe.

Efficiency is 30%= 30/100=0.3

hence the termal power will be= 103/ 0.3 =343.33 MW _(1)

Ans 2

The fission of 1 atom of U-235 generates 202.5 Mev= 3.24 X 10-11J.

Hence to generate the desired thermal power, the raction rate will be

=343.33 X 106/ 3.34 X 1011= 1.16 X 1020 per sec --(2)

Ans 3

From(2) The number of U-235 atoms disintegrates per sec =1.16X1020.

Hence, the number of U-235 stoms disintrated per year =1.16 X1020 X (365 X 86400sec) =5.20X 1027 ----(3)

Mass of U-235= 3.95 X10-25 Kg

Hence the mass required =( 5.20X 1027 )X (3.95 X10-25) Kg=2.055 X 10 3 Kg ---(4)

Ans 4

If the mass fraction of U235 is only 3%(=0.03 parts) then from equ(4) we get

0.03x =2.055 X 10 3 Kg

Hence,

x=68.5 X 10 3 Kg --(5)

This is the required mass of total uranium is 68.5 X 10 3 Kg.

Please note the question paper contains multiple questions. The answers of the 1st 4

are shown in details.

Here is the hints to solve the other parts.

Ans 5

from part 4, we see only 3% os the mass is used. The wastage is 97%

The nuclear waste=0.97X 68.5 X 10 3 Kg=66.4 X 10 3 Kg .

The density of uranium is 18900 Kg/m3

The corresponding volume V = mass/density=(66.4 X 10 3 /18900) m3=3.51m3

Ans 6

To produce 103 KWE the waste is 68.5 X 10 3 Kg with vol 3.51m3. hence the waste for 2.5X 1012 KW

will be = (3.51m3 / 103) X25X1012  

Ans 7

This is the volume. So this volume = sideX sideX side

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