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

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.

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Nho 5 years 2021-08-16T01:42:36+00:00 1 Answers 20 views 0

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  1. haidang
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    2021-08-16T01:44:23+00:00
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    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

           

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