IAEA/NVS/3

## Uranium consumption in a nuclear reactor

A typical **thermal reactor** contains about **100 tons** of uranium with an average enrichment of **2%** (do not confuse it with the enrichment of the **fresh fuel, **that is about 4%). For the reactor of power of **3000MW _{th}** determine the consumption of

**that must undergo fission each day to provide this thermal power.**

^{235}U**Solution:**

This problem can be solved very simply. The average recoverable energy per ^{235}U fission is about **E**_{r}** = 200.7 MeV/fission**. Since we know that each second we need **3000 MJ** of energy, the required reaction rate can be determined directly as:

Since each atom of ** ^{235}U** has a mass of 235u x 1.66 x 10

^{-27}kg/u = 3.9 x 10

^{-25}kg, the daily consumption of a reactor is:

9.33 x 10^{19} fissions/sec x 3.9 x 10^{-25} kg x 86400 sec/day = **3.14 kg/day**

For comparison, a 1000 MWe coal-fired power plant burns about 10 000 tons (about 10 million kg) of coal per day.

Since a typical fuel cycle takes about 320 days (12 month fuel cycle), the annual fuel consumption is about:

3.14 kg/day x 320 days = **1 005 kg of ^{235}U**

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