# Reactor Fuel and Waste

1. Jul 28, 2008

### LamyJamy

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?

b) Lets assume that all fission events are
What is the rate of fission events in the reactor core?

2. Relevant equations
E=mc2
P=E/t
m=mf-mi

3. The attempt at a solution
mf=235.0439u + 1.00867u
mf= 236.05259u

mi=143.92294u + 91.9261528u + 2(1.00867u)
mi=237.8664328u

m=mf-mi
m=237.8664428u - 236.05259u
m=1.8138428u

E=mc2
E=(1.8138428u)*((931.5Mev/c2)/u)*c2
E=1689.5945 Mev

1689.5945 Mev * 1.602E-19 J/ev = 2.707031447E-16 MJ

P=E/t
3333.33 MW = 2.707031447E-16 MJ / t
t = 8.120199E-20 s

Am I approaching the propblem correctly?

2. Jul 29, 2008

### LamyJamy

Oh these were the atomic masses given:
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
proton 1.00728 u
neutron 1.00867 u

3. Jul 29, 2008

### Dick

You are approaching it correctly in spirit. But why did you use the mass of Kr(92) in your problem when the statement says Kr(90), and then, I assume, reverse mi and mf to compensate??

4. Jul 29, 2008

### Dick

Zut, alors. That doesn't work. The mass of the initial state is still smaller than the final state. What's going on here? Are you sure of your table?

5. Jul 29, 2008

### Staff: Mentor

Power/(Energy/fission) gives rate of fissions. One must apply the appropriate units.

Try mi=235.0439u + 1.00867u (initial reactants)

mf=143.92294u + 89.9195238 u + 2(1.00867u) (final products)

These are switched

6. Jul 30, 2008

### Dick

Thanks, astronuc.

7. Jul 30, 2008

### LamyJamy

Thanks I got it now. =)
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