Complete Question
Use Stefan's law to find the intensity of the cosmic background radiation emitted by the fireball of the Big Bang at a temperature of 2.81 K. Remember that Stefan's Law gives the Power (Watts) and Intensity is Power per unit Area (W/m2).
Answer:
The intensity is [tex]I = 3.535 *10^{-6} \ W/m^2[/tex]
Explanation:
From the question we are told that
The temperature is [tex]T = 2.81 \ K[/tex]
Now According to Stefan's law
[tex]Power(P) = \sigma * A * T^4[/tex]
Where [tex]\sigma[/tex] is the Stefan Boltzmann constant with value [tex]\sigma = 5.67*10^{-8} m^2 \cdot kg \cdot s^{-2} K^{-1}[/tex]
Now the intensity of the cosmic background radiation emitted according to the unit from the question is mathematically evaluated as
[tex]I = \frac{P}{A}[/tex]
=> [tex]I = \frac{\sigma * A * T^4}{A}[/tex]
=> [tex]I = \sigma * T^4[/tex]
substituting values
[tex]I = 5.67 *10^{-8} * (2.81)^4[/tex]
[tex]I = 3.535 *10^{-6} \ W/m^2[/tex]
