Question

The spectral energy distribution of a star is maximum at twice temperature as that of sun. The total energy radiated by star is

• A. twice as that of the sun
• B. same as that of the sun
• C. sixteen times as that of the sun
• D. one-sixteenth of sun

Answer 1

Answer: (C)

sixteen times as that of the sun

Answer 2

From Stefan's law of radiation, the total radiant energy emitted per second per unit surface area of a black body is proportional to the fourth power of the absolute temperature $(T)$ of the body.
Therefore, $E=\sigma T^{4}$ where $\sigma$ is Stefan's constant.
Given, $T=2 T_{s}$
$\therefore E'=\sigma\left(2 T_{S}\right)^{4}$
$=16 \sigma T_{S}^{4}=16 E_{S}$
Hence, total energy radiated by star is sixteen times as that of the sun.