Answer:
3.00 x 10^-11 joules / atom of U-235
Step-by-step explanation:
We know that the formula for Power = Work done (w)/Time (t)
We need to get the joules from power , since Joules is the SI unit of work.
From the formula P = W/t
W = Power (P) * Time (t)
The SI unit for Time is seconds, hence we change 1 year in seconds
1yr * 365 days/yr * 24hrs/day * 60mins/hr * 60 secs/min = 31536000 secs
It was stated in the question that the plant operates at an efficiency of 40%,
Thus to get the true power we divide the power provided in the question by 0.4 or 40%
= X(0.4) = 1042MW
True Power X = 1042/0.4 = 2605MW
Thus true power = 2605 * 10^6 Watts
Now we have the time in seconds and true power in Watts, we then find the work done.
From our above formula P = W/t
W = P*t = (2605* 10^6) (31536000) =
Finally, we can solve for our energy (work):
P = W / T PT = W = (2880x10^6) (31536000) = 8.22 x 10^16 joules
We then calculate the amount of energy released by only 1 single uranium-235 atom.
= 8.22 x 10^16 joules / 1.07x10^6 g U-235 (235 g / 1 mol)(1 mol/6.0210^23 atoms)
= 3.00 x 10^-11 joules / atom of U-235