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jackster18
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Homework Statement
Approximately 1.0 X 10^34 J of energy is available from fusion of hydrogen in the world's oceans.
a) If 1.0 X 10^33 J of this energy were utilized, what would be the decrease in the mass of the oceans?
b) To what volume of water does this correspond?
Homework Equations
E=mc^2
Where E is the energy (in joules)
C is the speed of light (3.0 X 10^8 m/s (I think that’s it I looked it up))
m is the mass (in Kg)
V=m/d
Where V is the volume (in what units I don’t know)
m is the mass (in Kg)
d is the density (in what units I don’t know)
The Attempt at a Solution
a) ET("energy total", I’m calling it that because it’s the total energy in the world’s oceans from fusion of hydrogen)= 1.0 X 10^34 J
c= 3.0 X 10^8 m/s
m1(the mass of all the energy from the ocean)= ?
E=mc^2
ET=m1c^2
Rearranging for m1
m1= ET/c^2
= 1.0 X 10^34 J/ (3.0 X 10^8 m/s)^2
= 1.11 X 10^17 Kg
Therefore m1 (or the mass of the energy from the entire ocean) is 1.11 X 10^17 Kg.
Next part, finding the mass when 1.0 X 10^33 J of the energy is used:
E1(the amount of energy if utilized)= 1.0 X 10^33 J
c= 3.0 X 10^8 m/s
m2 (the mass of E1's energy) = ?
E=mc^2
E1=m2c^2
Rearranging for m2:
m2=E1/c^2
= 1.0 X 10^33 J / (3.0 X 10^8 m/s)^2
= 1.11 X 10^16 Kg
So m1= 1.11 X 10^17 Kg, and m2= 1.11 X 10^16 Kg
So the question said what would be the decrease in the mass of the oceans...so i guess i just subtract the two?
md(the mass decrease- i just made this up so i don't get the masses mixed up, so i put a d beside the m)= ?
md= m1 - m2
= 1.11 X 10^17 Kg - 1.11 X 10^16 Kg
= 9.99 X 10^16 Kg
I guess that’s the amount of mass decrease is 9.99 X 10^16 Kg. I’m not sure if I have done this correctly that’s why I’m asking.
Ok, now part b) To what volume of water does this correspond?
So I know that V= m/d
Somewhere I found on the internet that the density of water is 1 gram/mL...I’m not sure if that’s correct though, and if it is, can I just put mass (Kg) divided by (g/mL) to get volume? So what would the volume units be? Just mL I guess not too sure..
So the mass from before was 9.99 X 10^16 Kg, so:
m= 9.99 X 10^16 Kg
d= 1 g/mL (there is 1000 grams in a Kg...so 0.001 Kg/mL)
V=?
V = m/d
V= 9.99 X 10^16 Kg / 0.001 Kg/mL
V= 9.99 X 10^16 Kg/Kg/mL (the Kg's just cancel out i guess so its...
V= 9.99 X 10^16 mL
If you can help me I would greatly appreciate it. I’m in grade 12 physics and this is a question from an independent study unit. I just want to make sure I am correct or if I am understanding what’s going on, plus my teacher is marking it so...it would be nice to get it right.