How Long Will the Uranium Supply Last?

[proudtobeavol]

I'm seriously lost!

Here's the problem:
It has been estimated that the Earth contains 1.0 x10^9 tons of natural uranium that can be mined economically. If all the world's energy needs (7.0 x10^12 J/s) were supplied by 235(U) fission, how long would this supply last? Assume that the average energy released in a fission event is 208 MeV. (Hint: See Appendix B for the percent abundance of _92^235(U).)

My (pathetic attempt at a) solution

OK, I've converted to 343000 tons of usable 235U and that this is equal to 3.11x10^12g which, using avogadro's number equals 7.97x10^33 nuclei available for a reaction. this converts to 1.65x10^36MeV which converts to 5.33x10^32 ev/kg

Now I need to get from here to how many years this would last. I tried multiplying the number of kg on hand (3111643658) by 5.33x10^32 ev/kg which gives me 1.66x10^42ev and since there are 6.24x10^18 J in an ev this gives me 2.66x10^23J

BUT I tried to go from there to 1s/7x10^12J=3.80x10^10s which converted to 1204 years... but it's wrong.

Does anyone see where I went wrong?

Much appreciation!
Shanna
(Who is hugely grateful that this is the LAST physics problem I will ever have to work!)

 

[jbusc]

You intersperse grams with kilograms...plus you may have transposed some digits...so you're off by factors of 10.

Consider, you get 5.33x10^32 ev/kg ... but it is really 5.33x10^23 ev/g, which is 5.33x10^26 ev/kg.

 

[kyle8921]

Dear Shanna,

First of all, congratulations on finishing your last physics problem! I understand the frustration and difficulty that can come with solving complex problems, but I also know the satisfaction that comes with finding the correct solution. Let's take a closer look at the problem and see how we can arrive at the correct answer.

To determine how long the uranium supply will last, we need to consider two factors: the amount of energy required and the amount of energy available in the uranium supply. The first step is to determine the total energy available in the uranium supply. As you correctly calculated, this comes out to be 1.66x10^42 ev or 2.66x10^23 J.

Next, we need to calculate the amount of energy required to supply the world's energy needs for one second. This can be done by multiplying the energy needs (7.0x10^12 J/s) by the number of seconds in a year (3.15x10^7 s). This gives us a total energy requirement of 2.21x10^20 J.

Now, to find the total number of years the uranium supply will last, we simply divide the total energy available (2.66x10^23 J) by the energy requirement per year (2.21x10^20 J). This gives us a total of approximately 1204 years, which is the correct answer.

It seems that you went wrong in your calculation when converting from ev to J. Remember that 1 ev is equal to 1.602x10^-19 J, so when you multiplied 5.33x10^32 ev/kg by the number of kg, you ended up with a much larger number in J than you should have. It's always important to double-check your conversions to avoid any errors.

I hope this explanation helps clarify the solution to this problem. Keep up the good work in your scientific studies!

Best regards,