Answer:
5.327
Explanation:
Stefan-Boltzmann law states that the total radiant heat power emitted from a surface is proportional to the fourth power of its absolute temperature.
W = σT⁴
Where,
W is the total radiant heat power emitted from a surface
σ is constant of proportionality, called the Stefan–Boltzmann constant = 5.67 × 10⁻⁸ Wm⁻²K⁻⁴
T is absolute temperature in kelvin
For the first star, T = 5200 K
∴ W₁ = σ(5200)⁴
For the second star, T = 7900 K
∴ W₂ = σ(7900)⁴
The amount of energy radiated by the hotter star W₂, with respect to the other star W₁ is,
W₂ / W₁ = σ(7900)⁴ / σ(5200)⁴
[tex]\frac{W_{2}}{W_{1}} = \frac{79^{4}}{52^{4}}[/tex]
[tex]\frac{W_{2}}{W_{1}} = 5.327[/tex]
