The Total Power Output of the Sun Is$$4 \times 10 ^ { 26 } \mathrm {~W} \text {. Most of this energy is }$$

Question

Examlex · Accepted Answer

The Answer is The volume of the sun where most of the energy is produced is

\frac { 4 } { 3 } \pi r ^ { 3 } = ( 1.33 ) imes ( 3.14 ) imes \left( 1.75 imes 10 ^ { 8 } \mathrm {~m} ight) ^ { 3 } = 2.24 imes 10 ^ { 25 } \mathrm {~m} ^ { 3 }

The power produced per unit volume is (on the average)

\frac { 4 imes 10 ^ { 26 } \mathrm {~W} } { 2.24 imes 10 ^ { 25 } \mathrm {~m} ^ { 3 } } = 17.9 \mathrm {~W} / \mathrm { m } ^ { 3 }

For a reactor with an active volume of

10 imes 10 imes 10 \mathrm {~m} ^ { 3 }

the total power produced is

\left( 17.9 \frac { \mathrm { W } } { \mathrm { m } ^ { 3 } } ight) imes \left( 10 ^ { 3 } \mathrm {~m} ^ { 3 } ight) = 17.9 \mathrm {~kW}

This is negligible compared with realistic power reactor outputs. The p-p reaction is thus too slow (even under conditions as at the center of the sun) to make a useful reaction (this is good otherwise the sun would use up its source of energy too fast). Actually

17.9 \mathrm {~kW}

is equivalent to the combustion of about

0.5 \mathrm {~cm} ^ { 3 }

gasoline per second.

The Total Power Output of the Sun Is $4 \times 10 ^ { 26 } \mathrm {~W} \text {. Most of this energy is }$

Definitions:

The Total Power Output of the Sun Is 4×1026 W. Most of this energy is 4 \times 10 ^ { 26 } \mathrm {~W} \text {. Most of this energy is }4×1026 W. Most of this energy is

Definitions:

The Total Power Output of the Sun Is $4 \times 10 ^ { 26 } \mathrm {~W} \text {. Most of this energy is }$