College Physics:
College Physics:
11th Edition
ISBN: 9781305965515
Author: SERWAY, Raymond A.
Publisher: Brooks/Cole Pub Co
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Chapter 30, Problem 46AP

(a)

To determine

The energy produced.

(a)

Expert Solution
Check Mark

Answer to Problem 46AP

The energy produced is 3.61×1030J .

Explanation of Solution

Given info:

The mass of ocean is 1.32×1021kg

The mass per mol is 18.0×103kg/mol

The Avogadro number is 6.02×1023atoms/mol

The energy per atom 3.27MeV

The formula to calculate the number of water molecules is,

NH2O=(moceanMmol)NA

  • NH2O is the number of water molecules
  • mocean is mass of ocean water
  • NA is Avogadro number
  • Mmol is the mass per mole

The formula to calculate the number of deuterons is,

ND=2(1.56×104)NH20=2(1.56×104)(moceanMmol)NA

  • ND is the deuterons

The formula to calculate the number of events is,

Nevents=ND2=2(1.56×104)NH20=(1.56×104)(moceanMmol)NA

  • Nevents is the number of events

The formula to calculate the energy produced is,

E=NeventsE0=(1.56×104(moceanMmol)NA)E0

  • E is the energy
  • E0 is the energy of event

The mass of ocean is 1.32×1021kg

The mass per mol is 18.0×103kg/mol

The Avogadro number is 6.02×1023atoms/mol

The energy per atom 3.27MeV

Substitute 1.32×1021kg for mocean , 18.0×103kg/mol for Mmol , 6.02×1023atoms/mol for NA and 3.27MeV for E0 to find E .

E=(1.56×104(1.32×1021kg18.0×103kg/mol)(6.02×1023atoms/mol))(3.27MeV)(1.60×1013J1MeV)=3.61×1030J

Thus, the energy produced is 3.61×1030J .

Conclusion:

The energy produced is 3.61×1030J .

(b)

To determine

The time the energy lasts.

(b)

Expert Solution
Check Mark

Answer to Problem 46AP

The time the energy lasts is 1.63×108yr .

Explanation of Solution

Given info:

The rate of energy consumption is 7.00×1014J/s

The formula to calculate the time is,

t=EP

  • t is the time
  • P is the energy consumption rate

Substitute 3.61×1030J for E and 7.00×1014J/s for P to find t .

t=3.61×1030J(7.00×1014J/s)(3.156×107s1yr)=1.63×108yr

Thus, the time the energy lasts is 1.63×108yr .

Conclusion:

The time the energy lasts is 1.63×108yr .

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