   Chapter 32, Problem 42PE

Chapter
Section
Textbook Problem

Integrated Concepts(a) Estimate the years 1hat1he deuterium fuel in the oceans could supply the energy' needs of the world. Assume world energy consumption to be ten times that of the United States which is 8 × 10 19 J / y and the deuterium in the oceans could be converted to energy with an efficiency of 32%. You must estimate or look up the amount of water in the oceans and take the deuterium content to be 0.015% of natural hydrogen to find the mass of deuterium available. Note that approximate energy yield at deuterium is 3.37 × 10 14 J/kg .(b) Comment on how much time this is by any human measure. (It is not an unreasonable result, only an impressive one.)

To determine

(a)

The probable number of years that the deuterium fuel in the oceans could supply the energy needs of the world.

Explanation

Given:

Energy consumption of United states

EUS=8×1019J/y

Energy consumption of the world

E=10EUS

Energy yield of deuterium

ED=3.37×1014J/kg

Deuterium content in the water

0.015% of natural Hydrogen

Efficiency of energy conversion

η=32%

Volume of water in the Earth's oceans

V=1.332×109km3

( from U S geological survey)

Mass of deuterium atom

mD=3.3435×1027kg

Formula used:

Mass of water in the oceans is given by

M=ρV

Here, ρ is the density of water.

Calculation:

Express the volume of water in the oceans in m3.

V=1.332×109km3× 10 3 m 1 km3=1.332×1018m3

The density of water has a value of 1000 kg/m3.

Calculate the mass of the water in the oceans.

M=ρV=1000  kg/m31.332× 10 18m3=1.332×1021kg

Express the mass in grams.

M=1.332×1021kg×1000 g1 kg=1.332×1024g

It is known that there are 6.023×1023 molecules in 18.01528 g of water. Calculate the number of molecules in 1.332×1024g of water.

Nw= 6.023× 10 23 1.332× 10 24 g18.01528 g=4.45324×1046

Each water molecule has 2 hydrogen atoms. Calculate the number of hydrogen atoms in the sea water.

NH=2Nw=24.45324× 10 46=8

To determine

(b)

On how much the time of 800 billion years is by any human measure.

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