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Reactor Fuel and Waste

  1. Jul 28, 2008 #1
    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?
    Answer: 3333.33 MW

    b) Lets assume that all fission events are [​IMG]
    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. jcsd
  3. Jul 29, 2008 #2
    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
     
  4. Jul 29, 2008 #3

    Dick

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    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??
     
  5. Jul 29, 2008 #4

    Dick

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    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?
     
  6. Jul 29, 2008 #5

    Astronuc

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    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
     
  7. Jul 30, 2008 #6

    Dick

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    Thanks, astronuc.
     
  8. Jul 30, 2008 #7
    Thanks I got it now. =)
     
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