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

• chef99
In summary: So just to clarify, the conversion from watts to joules is simply multiplying by the amount of time (in seconds)? In summary, the nuclear power generating station produces 3.0 x109 watts of power which is equivalent to 7.776 x1015 joules over a period of 30 days. This amount of energy is converted from 86.4 grams of mass, assuming 100% efficiency.
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.

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.

gneill said:
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.

## 1. What is the mass to energy problem?

The mass to energy problem, also known as the mass-energy equivalence, is a concept in physics that states that mass and energy are interchangeable. This means that a certain amount of mass can be converted into an equivalent amount of energy, and vice versa.

## 2. Who first discovered the mass to energy problem?

The mass to energy problem was first discovered by Albert Einstein in 1905 through his famous equation, E=mc². This equation shows the relationship between energy (E), mass (m), and the speed of light (c).

## 3. Can we observe the conversion of mass to energy in everyday life?

Yes, we can observe the conversion of mass to energy in everyday life through nuclear reactions. For example, in a nuclear power plant, the energy produced from the splitting of atoms is a result of the conversion of mass to energy.

## 4. How is the mass to energy problem relevant in modern technology?

The mass to energy problem is highly relevant in modern technology, particularly in the field of nuclear energy and nuclear weapons. It is also important in understanding the behavior of particles in particle accelerators used in scientific research.

## 5. Is the mass to energy problem applicable to all forms of energy?

Yes, the mass to energy problem is applicable to all forms of energy, including kinetic energy, thermal energy, and potential energy. This is because all forms of energy have a corresponding mass according to Einstein's equation.

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