Consider sun as a black body whose interior consist of photons gas at T = 3×10^6k. Calculate the energy density of the solar radiations. Take (sigma) = 7.56×10^-16jm^-3k^-4
To calculate the energy density of solar radiation, we can use the Stefan-Boltzmann law, which relates the energy emitted by a black body to its temperature. The formula is as follows:
E = σT^4
Where:
E is the energy density of the radiation
σ is the Stefan-Boltzmann constant (given as 7.56×10^-16 J m^-3 K^-4)
T is the temperature of the black body (given as 3×10^6 K)
Substituting the given values into the equation:
E = (7.56×10^-16 J m^-3 K^-4) * (3×10^6 K)^4
Now we solve the equation step by step:
E = 7.56×10^-16 * 3^4 * (10^6)^4 J m^-3
E = 7.56×10^-16 * 81 * 10^24 J m^-3
E = 613.8 × 10^8 J m^-3
Hence, the energy density of solar radiation is approximately 613.8 × 10^8 J m^-3.