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

[LamyJamy]

In this problem, we're going get a rough estimate the amount of uranium fuel it would take if the US received 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 receives 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?
Answer: 3333.33 MW

b) Let's assume that all fission events are https://wug-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?

Homework Equations

E=mc2
P=E/t
m=mf-mi

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?

 

[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

 

[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??

 

[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?

 

[Astronuc]

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

90Kr 90.9234424 u
91Kr 89.9195238 u

 

[Dick]

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

Thanks, astronuc.

 

[LamyJamy]

Thanks I got it now. =)