Calculating Mass-Energy Conversion in a Nuclear Power Plant

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SUMMARY

The discussion focuses on calculating the mass-energy conversion in a nuclear power plant generating 3 x 10^9 W of power over a month (30 days). The formula used is m = E / c^2, where E is calculated as P x t. After correcting the time conversion from days to seconds, the final mass converted into energy is determined to be 0.0864 kg, demonstrating the importance of accurate unit conversion in physics calculations.

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  • Understanding of Einstein's mass-energy equivalence principle (E=mc²)
  • Knowledge of power units (Watts) and their relation to energy (Joules)
  • Ability to perform unit conversions, particularly between time units (seconds, hours, days)
  • Familiarity with basic physics concepts related to nuclear energy
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  • Study the implications of mass-energy equivalence in nuclear reactions
  • Learn about the efficiency of nuclear power plants and energy conversion processes
  • Explore advanced unit conversion techniques in physics problems
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Students studying physics, particularly those focusing on nuclear energy, engineers involved in power generation, and anyone interested in the principles of mass-energy conversion.

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Homework Statement


A nuclear power generating station generates 3 x 10^9 W of power. How much mass does the plant convert into energy in one month (30 days)? Assume that the process is 100% efficient.

2. The attempt at a solution
m = E / c^2, E = P x t
m = (3 x 10^9 W)(30 days) / (3 x 10^8 m/s) ^2
= 1 x 10^-6 kg
 
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Watts are equivalent to Joules per second. You've multiplied by 30 days. The units of time are not the same... so what should you do about that?
 
1 hr = 60 sec, 24 hr = 24 x 60 = 1440 s in a day, 1440 x 30 = 43200 s in 30 days
thus, (3 x 10^9 W)(43200 s) / (3 x 10^8 m/s) ^2 = 1.44 x 10^-3 kg
 
student07 said:
1 hr = 60 sec, 24 hr = 24 x 60 = 1440 s in a day, 1440 x 30 = 43200 s in 30 days
thus, (3 x 10^9 W)(43200 s) / (3 x 10^8 m/s) ^2 = 1.44 x 10^-3 kg
One hour is not 60 sec!
 
Omg I am so dumb lol, 60 min = 3600s, 86400 s in a day, 2,592,000 s in 30 days
thus, (3 x 10^9 W)(2,592,000 s) / (3 x 10^8 m/s) ^2 = 0.0864 kg
 
Huzzah! That's better! :smile:
 

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