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\5% 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?

P_thermal =

2) Lets assume that all fission events are

What is the rate of fission events in the reactor core?

R_fission =

3) What is the mass of ²³⁵U fissioned in one year?

Use =

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

Use_total =

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?

V_total =

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?

V_national =

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

L =

Answer 1

Date es Thermal power 343.336 o the total thermal feauxu genoualed by the seaclae bleekie power. 103 MW - 343.33 MWA @ the avenge energy released feu fisico is 200mle V The rate of fision es, R = 343-3390 = 1•0429xloffisiones 200 MeV 200x7-68164 ③ The mass of weanium - 235 required pee year NMA fr.0429x70bfissomasſa) (2359osoli) (Lyr) t NA 6OQBX1pmole (1007-29x1019 fissione/s) (2359)mole) (3-453x1075) = 1032x105g of The total mass of the fuel fee year is, 132x103g Mtotal 3.4% 5:5*100g year is mi 6.023x1023/mole D:D24