How Many Fission Reactions in a Year

AI Thread Summary
To determine the number of fission reactions in a year for a nuclear reactor operating at 778 MW, one must first calculate the total energy output over the year by multiplying the power by the total seconds in a year. The energy released per fission reaction is 183.9 MeV, which needs to be converted to joules for accurate calculations. By dividing the total energy output by the energy per fission reaction, the number of fission reactions can be found. This initial calculation also facilitates determining the amount of U-235 needed and the total change in mass over the year. Understanding the relationship between energy, time, and fission reactions is crucial for solving these problems effectively.
Ryo124
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Homework Statement



a - How many fission reactions would occur in 1 year of running of a nuclear reactor if the average power of the reactor is 778 MW?

b - How many kilograms of U-235 would be needed to run the reactor for 1 year?

c - What is the total change in mass for 1 year of running?

I've found that 183.9 MeV are released from one fission reaction.

Homework Equations



1 megawatt = 10^6 J/s (1,000,000 J/s)
1 eV = 1.602 ×10^−19 J
1 year = 31,556,926 sec
I don't know any others.

The Attempt at a Solution



I know that 778 MW = 778,000,000 J/s. I do not know where to go from there.
I'm not even sure if 183.9 MeV will be used in the answer to a, but I know the answer to a is required for b and b for c.

I've tried multiplying 778,000,000 J/s by 31,556,926 sec to get just Joules.
I've also tried dividing 778,000,000 J/s by 31,556,962 (don't know why - probably just out of desperation).
From here I've done a multitude of things (such as dividing this answer by 1.602E-13 J) but nothing I've done is working. Someone please help, I've been at this one since 12:30 (now 4:30) and it's really getting me frustrated.

- edit: 6:30pm - still working on this one, tried tons of Google searches to no avail, also posted on some other forums (although I don't know why -this one is the best :redface:)
Still can't get answer, someone please explain/help/respond!
 
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You want a total output of power over a year. You know the total time period, and the rate at which the reactor outputs energy. You then use the amount of energy released in each reaction.
(If you need a further hint, think about the dimensions: energy/time, time, energy/reaction. If they were simply fractions how would you find the term reaction knowing energy/time, time and energy/reaction? )
 
Multiplying power by time to get joules is the right first step. Then you divide that by the energy of a single fission reaction. Convert 183.9MeV to Joules. It's 183.9 times your 1.602*10^(-13) J.
 
Thanks guys, sorry I had to PM ya, but I thought with such a nicely written question (in my opinion) I would get a quicker response (guess it was still pretty quick).

I knew I had to divide "A" by "A" to get a number, so that is what I was working towards, it makes much more sense now.
(energy/time x time = energy; then energy divided by reaction, which is 183.9 MeV)

As for the other parts, the answers were clear once i had part "a". Thank you :smile:
 
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