How many kg Uranium is needed for 5kW produced?

In summary: I solved for the energy released to be 5.6MeV and I know that E = Pt, but I'm not sure how to find the amount of mass needed to produce that much power.In summary, to produce 5kW of power from Uranium with a half-life of 87.7 years, you need to release 5.6MeV of energy. Using the equation E = Pt, you can calculate the amount of decays per second needed to produce this power. However, you will also need to convert units to find the amount of mass required.
  • #1
Narud
1
0
Member advised to show more effort in the attempt at solution.

Homework Statement



Energy released is 5.6MeV, 5kW is produced, Half life = 87.7 years for Uranium
Need to find how many kg you need to produced that much power.

Homework Equations



E = Pt, Q = (mass defect) * 931.5MeV/c^2

The Attempt at a Solution



I solved for the energy released to be 5.6MeV as stated above, except I'm not sure how to find the amount required for that power produced...
 
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  • #2
Narud said:

Homework Statement



Energy released is 5.6MeV, 5kW is produced, Half life = 87.7 years for Uranium
Need to find how many kg you need to produced that much power.

Homework Equations



E = Pt, Q = (mass defect) * 931.5MeV/c^2

The Attempt at a Solution



I solved for the energy released to be 5.6MeV as stated above, except I'm not sure how to find the amount required for that power produced...
If I'm not wrong, are you the same person https://physics.stackexchange.com/q/382031/149663?

The two questions match amazingly.
 
  • #3
Wrichik Basu said:
If I'm not wrong, are you the same person https://physics.stackexchange.com/q/382031/149663?

The two questions match amazingly.
Including the fact that the question seems to be about Plutinium 238 wich does have a half-life of 87.7 years.
Stackexchange wants you to show some effort on homework questions as well.

Since you know how much energy one decay produces, it should be easy to compute how many decays/second you need to get a certain power. You only need to convert some units.
 
  • #4
willem2 said:
Stackexchange wants you to show some effort on homework questions as well.
True.
 

1. How is the amount of uranium needed for 5kW produced calculated?

The amount of uranium needed for 5kW produced is calculated by dividing the power output (5kW) by the specific energy of uranium (19,400,000,000 joules per kilogram). This calculation results in approximately 0.000000000258 kilograms of uranium.

2. How much uranium is needed to produce 5kW for one hour?

To produce 5kW for one hour, the amount of uranium needed would be 0.0000009 kilograms. This is calculated by multiplying the power output (5kW) by the time (1 hour) and dividing by the specific energy of uranium.

3. What is the specific energy of uranium?

The specific energy of uranium is the amount of energy produced per unit mass of uranium. It is measured in joules per kilogram and is approximately 19,400,000,000 joules per kilogram for uranium.

4. How does the amount of uranium needed for 5kW produced compare to other energy sources?

The amount of uranium needed for 5kW produced is relatively small compared to other energy sources. For example, to produce the same amount of power, approximately 0.000000000258 kilograms of uranium is needed, while 0.02 kilograms of coal or 0.00000000018 kilograms of natural gas would be needed.

5. Is the amount of uranium needed for 5kW produced the same for all nuclear reactors?

No, the amount of uranium needed for 5kW produced may vary depending on the type of nuclear reactor being used. Some designs may be more efficient and require less uranium, while others may require more. Additionally, the age and condition of the reactor can also affect the amount of uranium needed.

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