Calculating Mass-Energy Conversion in a Nuclear Power Plant

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A nuclear power plant generating 3 x 10^9 W converts mass into energy based on the equation m = E/c^2. The energy produced over 30 days is calculated by multiplying power by time, converting time into seconds for accuracy. Initially, incorrect time conversions led to an erroneous mass calculation, but after correcting the time to 2,592,000 seconds, the mass converted is determined to be 0.0864 kg. The discussion highlights the importance of unit consistency in calculations. Accurate mass-energy conversion is crucial for understanding nuclear power efficiency.
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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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