How Much Mass Converts to Energy in a Nuclear Plant Over a Month?

[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]

Homework Equations

E = mc²

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 x10⁶s in 30 days.

E_J = P_w + t_s

E_J = (3.0 x10⁹ w)(2.592 x10⁶s)

E_J = 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.

 

[gneill]

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.