- #1

chef99

- 75

- 4

## Homework Statement

A nuclear power generating station generates 3.0 x10

^{9}W of power. How much mass does the plant convert into energy each month (30 days)? Assume that the process is 100% efficient[/B]

## Homework Equations

E = mc

^{2}

E

_{J}= (P

_{w})( t

_{s})

## The Attempt at a Solution

First determine the amount of energy in joules, converting from watts.

There are 2.592 x10

^{6}s in 30 days.

E

_{J}= P

_{w}+ t

_{s}

E

_{J}= (3.0 x10

^{9}w)(2.592 x10

^{6}s)

E

_{J}= 7.776 x10

^{15}J

Now solve for the mass to energy conversion

E = mc

^{2}

m = E / c

^{2}

m = 7.776 x10

^{15}J / (3.0 x10

^{8})

^{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 x10

^{9}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.