A nuclear power generating station generates 3.0 x109 W of power. How much mass does the plant convert into energy each month (30 days)? Assume that the process is 100% efficient[/B]
E = mc2
EJ = (Pw)( ts)
The Attempt at a Solution
First determine the amount of energy in joules, converting from watts.
There are 2.592 x106s in 30 days.
EJ = Pw + ts
EJ = (3.0 x109 w)(2.592 x106s)
EJ = 7.776 x1015 J
Now solve for the mass to energy conversion
E = mc2
m = E / c2
m = 7.776 x1015 J / (3.0 x108)2
m = 0.0864 kg
m = 86.4 g
86.4 g of mass was converted into energy in 30 days.
I know the amount of mass needed for large amounts of energy, but this seems to be a very small amount. The one thing I'm not sure about is the conversion from watts to joules, as my course didn't provide a specific equation to do this. All of the questions I've done have been in joules already. The other thing is I did these calculations assuming the 3.0 x109 Watts of power produced is over 30 days, as the question doesn't specify over what period that energy is produced. I used 30 days as that was the only timeframe given for any of the measurements. I don't know if this is the correct assumption to make or not. I would really appreciate it if someone could take a look at this, specifically the watts to joules conversion. Thanks.