What initial mass of 235U is required to operate a 650-MW reactor for 1 year? Assume 40% efficiency.
The amount of heat that must be generated by the fission reaction is 650*10^6/0.4 Watts. Multiply that by the number of seconds in a year to get the number of Joules of heat required.
Then divide that by the amount of heat released in a typical U235 fission.
This website may help:
http://hyperphysics.phy-astr.gsu.edu/HBASE/nucene/u235cs.html#c1
That will tell you how many U235 atoms must fission. Convert that number to mass, using the mass of a U-235 atom, which is 235/Nav grams. Nav is Avogadro's number
To calculate the initial mass of 235U required to operate a reactor, we need to follow these steps:
Step 1: Determine the energy produced by the reactor in one year.
Step 2: Calculate the energy obtained from one mole of 235U.
Step 3: Determine the number of moles of 235U required for the energy produced by the reactor in one year.
Step 4: Convert the number of moles to grams using the molar mass of 235U.
Let's tackle each step one by one:
Step 1: Determine the energy produced by the reactor in one year.
The power output of the reactor is given as 650 MW (megawatts) and the time of operation is one year. To obtain the energy produced, we need to convert MW to energy units (Joules):
1 MW = 1 million joules per second
So, the energy produced by the reactor in one year can be calculated as follows:
Energy = Power × Time
Energy = 650 MW × (365 days × 24 hours/day × 3600 seconds/hour)
Step 2: Calculate the energy obtained from one mole of 235U.
First, we need to determine the energy released per fission event (in Joules) for 235U. This information can be found in nuclear physics references as 3.2×10^-11 Joules per fission.
Step 3: Determine the number of moles of 235U required for the energy produced by the reactor in one year.
To determine the moles of 235U required, we divide the energy produced by the reactor in one year by the energy released per fission event:
Moles of 235U = Energy produced by the reactor / Energy released per fission event
Step 4: Convert the number of moles to grams using the molar mass of 235U.
To convert the moles of 235U to grams, multiply the number of moles by the molar mass of 235U, which is approximately 235 grams per mole.
By following these steps, you can calculate the initial mass of 235U required to operate a 650 MW reactor for 1 year, with 40% efficiency.