In this problem, we\'re going get a rough estimate of the amount of uranium fuel
ID: 2154792 • Letter: I
Question
In this problem, we're going get a rough estimate of 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 is normally given as the 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 requires 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? P thermal = 3333.33 MW
b) Lets assume that all fission events are https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/Phys1202/summer/homework/Ch-32-Nuclear-Physics/fuel_amount_algebra/fission_equation.jpg
What is the rate of fission events in the reactor core? R fission = 1.16E20/sec
c) What is the mass of 235U fissioned in one year? Use = ??? kg
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 3% of the fuel is actually 235U by mass.
What is the total mass of fuel that is used in one year? Use total = ??? kg
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? V total = ??? m^3 (HELP: Recall that the density of the uranium can be estimated at 19,000 kg/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? V national = ??? m^3
g) If this waste were formed into a cube, what would be the length of the cube's sides? L = ??? m
I figured out a) and b) which took me forever, but am having a very difficult time with c,d,e,f, and g. Any help would be greatly appreciated. Thank you in advance.
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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