# Homework Help: How Many Fission Reactions in a Year

1. Dec 1, 2007

### Ryo124

1. The problem statement, all variables and given/known data

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.

2. Relevant 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.

3. 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 )

Last edited: Dec 1, 2007
2. Dec 1, 2007

### muppet

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? )

3. Dec 1, 2007

### Dick

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.

4. Dec 1, 2007

### Ryo124

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

Last edited: Dec 1, 2007