Calculating Mass-Energy Conversion in a Nuclear Power Plant

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In summary, a nuclear power generating station with a power output of 3 x 10^9 W can convert 0.0864 kg of mass into energy in one month (30 days), assuming 100% efficiency. This was calculated using the equation m = E / c^2, where E = P x t and adjusting for the correct units of time.
  • #1
student07
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1

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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  • #2
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?
 
  • #3
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
 
  • #4
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!
 
  • #5
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
 
  • #6
Huzzah! That's better! :smile:
 

1. What is the theory of relativity?

The theory of relativity is a fundamental principle in physics that describes how the laws of physics are the same for all observers in uniform motion. It is comprised of two theories: the special theory of relativity, which explains the relationship between space and time for objects in constant motion, and the general theory of relativity, which explains the relationship between gravity and the curvature of spacetime.

2. What are the implications of relativity?

The implications of relativity are far-reaching and have greatly impacted our understanding of the universe. They include the concept of time dilation, where time moves slower for objects in motion; the equivalence of mass and energy, described by E=mc2; and the bending of light near massive objects, such as stars.

3. How does relativity affect our daily lives?

Although relativity may seem like a complex theory that only applies to extreme circumstances, it actually has significant impacts on our daily lives. For example, the GPS systems we use rely on the principles of relativity to accurately calculate our location and time. Additionally, many medical technologies, such as MRI machines, also use relativity to function.

4. Are there any limitations to the theory of relativity?

While the theory of relativity has been confirmed through numerous experiments and observations, it does have limitations. It does not fully explain the behavior of subatomic particles or the force of gravity at the quantum level. Scientists are still working to reconcile relativity with quantum mechanics in a unified theory.

5. Why is the theory of relativity important for scientific research?

The theory of relativity is important for scientific research because it provides a foundational understanding of the fundamental laws of physics. It has also led to groundbreaking discoveries and advancements, such as the confirmation of the existence of black holes and the prediction of gravitational waves. Relativity continues to play a crucial role in shaping our understanding of the universe and driving scientific progress.

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