# How much uranium-235 does a nuclear power generator consume to generate 1.5 GW?

• swilson31
This is about 500,000 kg of U-235. So the result of 569 kg seems reasonable.In summary, the total thermal power generated in a nuclear power reactor is 1.5 GW. To find out how much uranium-235 is consumed in a year, one must first determine the total energy used in a year. This can be found by multiplying the power by the time. Then, knowing the energy per fission of U-235 and the mass of 1 atom, one can calculate the number of fissions needed and the weight of U-235 used. For a 1.5 GW reactor, the weight of U-235 used in a year would be approximately 569 kg.
swilson31
SOLVED
thank you for the help

## Homework Statement

The total thermal power generated in a nuclear power reactor is 1.5 GW.
How much uranium-235 does it consume in a year?

m(235U)=-----kg

E=mc2

## The Attempt at a Solution

E=mc2
1.5*109J*60sec*60min*24hr*365days=m*(3*108m/s)2

Solving for m leaves me with .53 kg which come up incorrect in Mastering Physics.

Last edited:
Hi there,

0.53kg is the mass transformed into energy, not the amount of U-235 needed to sustain a 1.5GW nuclear fission reaction.

To find out how much U-235 you need, you must get the total amount of energy (which you seem to have correct in your equation). Then, how energy is liberated in each fission of U-235 atom can help you find out how many reactions are needed to sustain this power output. Having that number, you can evaluate the number of matter (moles) needed, and then the mass of U-235.

This calculation is a bit simplist but it would give a gross estimate of what is going on in a nuclear reactor.

Cheers

A fission reaction does not annihilate all the matter, only a small fraction of the mass of the uranium 235 will be converted into energy. You need to know the starting mass and the mass of the products.

swilson31 said:

## Homework Statement

The total thermal power generated in a nuclear power reactor is 1.5 GW.
How much uranium-235 does it consume in a year?

m(235U)=-----kg

E=mc2

## The Attempt at a Solution

E=mc2
1.5*109J*60sec*60min*24hr*365days=m*(3*108m/s)2

Solving for m leaves me with .53 kg which come up incorrect in Mastering Physics.
The approach is correct, but some steps are missing.

One must determine the energy E used in a year. E = Power (average) * time, so J = W * s.

Then one must realize the energy per fission, fission consumes 1 atom and the mass of 1 atom. Fission of U-235 produces ~200-205 MeV/fission. (This is fine if one does not consider the contribution of Pu-239/Pu-240/Pu-241 which builds up slowly during operation in commercial reactor.)

So total energy=1.5e9*60*60*24*365=4.73e16 J
Fission of one atom of u-235=3.244e-11 J
Fissions needed: total energy/fission of one atom=1.46e27
weight of one u-235 atom:3.9e-25 kg
weight of u-235 used: 1.46e27*3.9e-25 kg= 569.4 kg

is this correct?

Method is correct, and result seems to be correct.

This of course assumes that the 1.5 GW is thermal energy, which would be a small reactor.

If 1.5 GW is electrical energy, and the process is about 33% efficient, then the thermal energy would be about 4.5 GW, and the amount of U-235 would be 3 * 569 kg.

A large 3.5 GWt reactor has a core size of about 100 MT or 100,000 kg of fuel.

## 1. How much uranium-235 is needed to generate 1.5 GW of power?

The amount of uranium-235 needed to generate 1.5 GW of power depends on several factors, such as the efficiency of the nuclear power plant and the type of reactor used. However, on average, a nuclear power generator consumes about 27 metric tons of uranium-235 per year to produce 1.5 GW of power.

## 2. How does the amount of uranium-235 consumed compare to other sources of energy?

In terms of energy output, nuclear power is much more efficient than other sources of energy such as coal or natural gas. For example, a coal power plant would need to burn about 3 million metric tons of coal to produce the same amount of energy as a nuclear power plant using 27 metric tons of uranium-235.

## 3. How long does the uranium-235 fuel last in a nuclear power generator?

The lifespan of the uranium-235 fuel in a nuclear power generator varies depending on the type of reactor and its operational efficiency. On average, a reactor can operate for 18-24 months before needing to refuel with new uranium-235.

## 4. Is the consumption of uranium-235 a sustainable energy source?

While uranium-235 is a non-renewable resource, it is considered a sustainable energy source because of its high energy output and the fact that it can be recycled. Additionally, advancements in nuclear technology have made it possible to extract more energy from a smaller amount of uranium-235, making it a more sustainable option.

## 5. Are there any safety concerns with the consumption of uranium-235 in nuclear power generators?

As with any form of energy production, there are potential safety concerns with the use of uranium-235 in nuclear power generators. However, strict regulations and safety measures are in place to ensure the safe operation of nuclear power plants and minimize the risk of accidents. Additionally, advancements in technology have made nuclear power plants even safer and more efficient.

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