The average energy released in the fission of a single uranium-235 nucleus is about 3. 10-11 J. If the conversion of this energy to electricity in a nuclear power plant is 45% efficient, what mass of uranium-235 undergoes fission in a year in a plant that produces 2000 megawatts
200Mev
To solve this problem, we need to calculate the mass of uranium-235 that undergoes fission in a year in a power plant that produces 2000 megawatts of electricity.
Step 1: Convert the power output to watts:
2000 megawatts = 2000 x 10^6 watts.
Step 2: Calculate the energy produced in one year:
The energy produced in one year can be found using the formula:
Energy produced = Power x Time.
Since we know the power and need to find the energy produced in a year, we need to convert the time to seconds:
One year = 365 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute.
Now, we can calculate the energy:
Energy produced = (2000 x 10^6 watts) x (365 days x 24 hours x 60 minutes x 60 seconds).
Step 3: Calculate the number of uranium-235 nuclei undergoing fission:
We know that the average energy released per fission of a uranium-235 nucleus is 3 x 10^-11 J.
Number of fissions = Energy produced / Energy per fission.
Step 4: Calculate the mass of uranium-235 undergoing fission:
The mass of uranium-235 undergoing fission can be calculated using the formula:
Mass = (Number of fissions x Molar mass of uranium-235) / Avogadro's number.
The molar mass of uranium-235 is 235 g/mol, and Avogadro's number is 6.02 x 10^23.
Now, let's calculate:
Mass = (Number of fissions x 235 g/mol) / (6.02 x 10^23).
Note: We need to convert grams to kilograms by dividing by 1000 to get the final answer in kilograms.
The mass of uranium-235 undergoing fission in a year in a power plant that produces 2000 megawatts of electricity is:
Mass = [(2000 x 10^6 watts) x (365 days x 24 hours x 60 minutes x 60 seconds) x 235 g/mol] / (6.02 x 10^23) / 1000 kg.
To find the mass of uranium-235 that undergoes fission in a year, we need to first calculate the total energy produced by the nuclear power plant in a year using the given power output.
Step 1: Convert the power output to watts:
2000 megawatts = 2000 x 10^6 watts
Step 2: Calculate the total energy produced in one year:
Energy = Power x Time
Assuming a year has 365 days and each day has 24 hours:
Energy = (Power in watts) x (Time in seconds)
= (2000 x 10^6 watts) x (365 days) x (24 hours/day) x (3600 seconds/hour)
Step 3: Calculate the total energy produced in one year:
Energy = (2000 x 10^6) x (365 x 24 x 3600) joules
Step 4: Calculate the number of uranium-235 nuclei that undergo fission:
Number of nuclei = Total energy produced / Energy released per nucleus
= (2000 x 10^6) x (365 x 24 x 3600) joules / (3 x 10^-11) joules
Step 5: Calculate the mass of uranium-235 that undergoes fission:
Mass = Number of nuclei x Mass per nucleus
Mass = Number of nuclei x Atomic mass of uranium-235
To get the atomic mass of uranium-235, we can refer to the periodic table or use the value 235 grams/mol.
Step 6: Calculate the mass of uranium-235 that undergoes fission in one year:
Mass = (Number of nuclei x Atomic mass of uranium-235) / Avogadro's number
Now, we have all the values required to calculate the mass of uranium-235 that undergoes fission in a year.