The sun generates energy through nuclear fusion, which converts mass into energy. If the sun radiates $3.8 \times 10 ^ { 26 } \mathrm {~W}$ of power, calculate the rate at which the sun loses mass (i.e., kg/s).

Question

Quizplus · Accepted Answer

The Answer is The change in mass is given by Einstein's relation as

\Delta m = E / c ^ { 2 }

So the rate of change of mass is

\Delta m / \Delta t = [ E / \Delta t ] / c ^ { 2 } = P / c ^ { 2 }

Converting the power radiated by the sun to

\mathrm { MeV } /

s gives

3.8 imes 10 ^ { 26 } \mathrm {~W} = \left( 3.8 imes 10 ^ { 26 } \mathrm {~J} / \mathrm { s } ight) / \left( 1.6 imes 10 ^ { - 13 } \mathrm {~J} / \mathrm { MeV } ight) = 2.38 imes 10 ^ { 36 } \mathrm { MeV } / \mathrm { s }

The rate of change of mass will be

\Delta m / \Delta t = \left( 2.38 imes 10 ^ { 36 } \mathrm { MeV } / \mathrm { s } ight) / ( 931.494 \mathrm { MeV } / \mathrm { u } ) = 2.55 imes 10 ^ { 36 } \mathrm { u } / \mathrm { s }

Converting to

\mathrm { kg } / \mathrm { s }

gives

\left( 2.55 imes 10 ^ { 36 } \mathrm { u } / \mathrm { s } ight) imes \left( 1.66 imes 10 ^ { - 27 } \mathrm {~kg} / \mathrm { u } ight) = 4.2 imes 10 ^ { 9 } \mathrm {~kg} / \mathrm { s }

The Sun Generates Energy Through Nuclear Fusion, Which Converts Mass 3.8×1026 W3.8 \times 10 ^ { 26 } \mathrm {~W}3.8×1026 W

The Sun Generates Energy Through Nuclear Fusion, Which Converts Mass $3.8 \times 10 ^ { 26 } \mathrm {~W}$