Question

a proposed nuclear reactor facility will have an electrical power output of 855 mw with a 35.9% efficiency in converting nuclear to electrical power. assuming the average fission reaction produces 193 mev, how many reactions will take place at the facility every second?

Answer 1

To determine the number of nuclear fission reactions per second, calculate the thermal power output in joules per second using the electrical power output and efficiency. Then, convert the energy produced per fission reaction into joules and divide the thermal power by the energy per reaction.

Step-by-step explanation:

You're asking how many fission reactions will take place every second in a proposed nuclear reactor facility with a power output of 855 MW and 35.9% efficiency. First, let's calculate the total amount of energy produced by the reactor per second (its thermal power output) based on its electrical output and efficiency. We use the formula:

Thermal Power Output = Electrical Power Output / Efficiency

Plugging in your numbers gives us: Thermal Power Output = 855 MW / 0.359 => Thermal Power Output ≈ 2381.62 MW

Now, we convert this megawatt value to megajoules per second (MJ/s), noting that 1 MW equals 1 MJ/s. So, the reactor produces approximately 2381.62 MJ per second.

Since each fission reaction produces 193 MeV of energy, we must convert this to joules to match our power output units. Remember that 1 eV = 1.602 x 10^-19 joules, so:

Energy per Reaction = 193 MeV * (1.602 x 10^-19 J/eV)

Finally, to find the number of reactions per second:

Number of Reactions per Second = Thermal Power Output (J/s) / Energy per Reaction (J)

By solving this equation, we can find the total number of fissions occurring each second.