Explanation Write the expression from the Boltzmann distribution function gives the fraction of the photons that have energy between E and E + d E . The fraction that have energy between E and infinity. ∫ E ∞ e − E / k B T d E ∫ E ∞ e − E / k B T d E = ∫ E ∞ e − E / k B T ( − d E / k B T ) ∫ E ∞ e − E / k B T d E ( − d E / k B T ) (I) Here, E is the energy of the particle, k B is the Boltzmann constant, and T is the temperature. Rewrite the above equation. ∫ E ∞ e − E / k B T d E ∫ E ∞ e − E / k B T d E = [ e − E / k B T ] E ∞ [ e − E / k B T ] E ∞ = e − E / k B T (II) Conclusion: Substitute 1

Principles of Physics: A Calculus-Based Text

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Chapter 31, Problem 63P

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The temperature of the 1.00% population of photons.

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Chapter 31, Problem 62P

Chapter 31, Problem 64P

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Chapter 31 Solutions

Principles of Physics: A Calculus-Based Text

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The temperature of the 1.00% population of photons.

Solution Summary: The author writes the expression from the Boltzmann distribution function gives the tion of the photons that have energy between E and E+dE.

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