High School

We appreciate your visit to What is the approximate power output of a tex 235 92 text U tex reactor if it takes 30 days to use up 2 kg. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

What is the approximate power output of a [tex]^{235}_{92}\text{U}[/tex] reactor if it takes 30 days to use up 2 kg of fuel, and each fission gives 185 MeV of usable energy?

Answer :

To determine the approximate power output of the reactor, we will follow these steps:


  1. Calculate the Energy Produced per Fission:


    • Each fission of a uranium-235 ([tex]^{235}_{92}U[/tex]) nucleus releases 185 MeV of energy.


    • Convert this energy to joules (J). Note that 1 eV = $1.602 \times 10^{-19}$ J, so:

      [tex]185 \text{ MeV} = 185 \times 10^6 \text{ eV} \times 1.602 \times 10^{-19} \text{ J/eV}[/tex]

      [tex]185 \text{ MeV} = 2.9637 \times 10^{-11} \text{ J}[/tex]




  2. Determine the Number of Fissions in 2 kg of [tex]^{235}_{92}U[/tex]:


    • The molar mass of uranium-235 is approximately 235 g/mol.


    • Calculate the number of moles in 2 kg:

      [tex]\text{Number of moles} = \frac{2000 \text{ g}}{235 \text{ g/mol}} \approx 8.51 \text{ mol}[/tex]


    • Use Avogadro's number ($6.022 \times 10^{23}$ atoms/mol) to calculate the total number of atoms in 2 kg:

      [tex]\text{Number of atoms} = 8.51 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol}[/tex]

      [tex]\approx 5.12 \times 10^{24} \text{ atoms}[/tex]




  3. Calculate the Total Energy Produced:


    • Multiply the number of fissions by the energy per fission:

      [tex]\text{Total energy} = 5.12 \times 10^{24} \times 2.9637 \times 10^{-11} \text{ J}[/tex]

      [tex]\approx 1.517 \times 10^{14} \text{ J}[/tex]




  4. Find the Power Output:


    • Power is the rate of energy consumption over time.


    • Convert 30 days to seconds (since 1 day = 24 hours, 1 hour = 3600 seconds):

      [tex]30 \text{ days} = 30 \times 24 \times 3600 \text{ seconds} = 2.592 \times 10^6 \text{ seconds}[/tex]


    • Use the power formula, [tex]P = \frac{E}{t}[/tex]:

      [tex]P = \frac{1.517 \times 10^{14} \text{ J}}{2.592 \times 10^6 \text{ seconds}}[/tex]

      [tex]\approx 5.85 \times 10^7 \text{ W}[/tex]





Therefore, the approximate power output of the [tex]^{235}_{92}U[/tex] reactor is 58.5 MW (megawatts).

Thanks for taking the time to read What is the approximate power output of a tex 235 92 text U tex reactor if it takes 30 days to use up 2 kg. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada