Calculating Mass-Energy Conversion in a Nuclear Power Plant

[student07]

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

 

[gneill]

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?

 

[student07]

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

 

[gneill]

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!

 

[student07]

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

 

[gneill]

Huzzah! That's better!

 

[student07]

Since you are here can you also help me with this https://www.physicsforums.com/threads/spaceship-problem.816803/#post-5127239
thank you!