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Old Apr 12th 2014, 03:04 PM   #1
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Exclamation Help Please !!

I'm doing a practice test for my physics assessment tomorrow and i cant figure out this question even with the answers.

The energy released during the reaction is 2.724x10^-11 J. A nuclear power plant has an output of 8.21 GW (8.21x10^9 W). Calculate the minimum mass of uranium 235 that would be used every hour. (The mass of an atom of uranium 235 is 390.3x10^-27 kg)

The answer is

To produce 8.21x10^9 J of energy, 8.21x10^9/ 2.724x10^-9 = 3.0140x10^20 reactions must occur. Each reaction involves 1 atom of uranium, so in one second :
m= 3.0140 x 10^20 x 390.3 x 10^-27
= 1.1764 x 10^-4kg

In 1 hour, m= 1.1764 x10^-4 x 60 x 60 = 0.423kg

Can someone please just walk me through how they got these figures in these places and what formulas were actually used. Thanks.
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Old Apr 13th 2014, 05:24 AM   #2
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It helps to carefully apply the units of measurement to these figures. The first piece of data is that one atomic reaction yields 2.724 x 10^-11 Joules, so the rate of energy release is 2.724 x10^-11 J/reaction. The second bit of data is the plant generates 8.21 x 10^9 watts of energy. You need to know that 1 watt = 1 Joule/second, so the power output is 8.21x10^9 J/s. Note from the units that if you divide the second number by the first you get units of (J/s)/(J/reaction) = reactions/s (note how the Joule terms cancel). Hence (8.21x10^9 J/s)/2.724x10^-11 J/reaction) = 3.01x10^20 reactions/s.

Each reaction takes one atom, so the mass of atoms per second is:

3.01x10^20 reactions/s x 1 atom/reaction x 390.2x10^-27Kg/atom= 1.18x10^-4 Kg/s.

Again - note that by writing out the units it becomes clear why these numbers are multiplied the way they are.

To convert from Kg/s to Kg/hour you multiply by the number of seconds per hour:

1.18x10^-4 Kg/s x 60 s/min x 60 min/Hr = 0.423 Kg/Hr.

Hope this helps!
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