# Mass to energy problem

chef99

## Homework Statement

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.

Mentor
Hi chef99,

Your work looks correct. Lots of energy is tied up in very little mass.

A Watt is a unit of power, the rate at which energy is expended (or absorbed). It is in fact a composite unit, comprising energy and time:

##W = \frac{Joule}{sec}##

So you can see how multiplying the Watts by the amount of time will give you the total energy produced over that period of time.

chef99
Hi chef99,

Your work looks correct. Lots of energy is tied up in very little mass.

A Watt is a unit of power, the rate at which energy is expended (or absorbed). It is in fact a composite unit, comprising energy and time:

##W = \frac{Joule}{sec}##

So you can see how multiplying the Watts by the amount of time will give you the total energy produced over that period of time.

Ok thank you for your help.