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.

Answer 1

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 $I = 3.535 *10^{-6} \ W/m^2$

Explanation:

From the question we are told that

    The temperature is  $T = 2.81 \ K$

Now  According to Stefan's law

        $Power(P) = \sigma * A * T^4$

Where  $\sigma$ is the Stefan Boltzmann constant with value  $\sigma = 5.67*10^{-8} m^2 \cdot kg \cdot s^{-2} K^{-1}$

  Now the intensity of the cosmic background radiation emitted according to the unit from the question is mathematically evaluated as

        $I = \frac{P}{A}$

=>      $I = \frac{\sigma * A * T^4}{A}$

=>      $I = \sigma * T^4$

substituting values

      $I = 5.67 *10^{-8} * (2.81)^4$

       $I = 3.535 *10^{-6} \ W/m^2$