 Solution

ID: past-exam-of-the-short-options-paper-shared-by-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2019/s16/1/b/solution

One mole of original atoms contains

(1 - ζ)

moles of neutral atoms,

ζ

moles of protons and

ζ

moles of electrons. All are monatomic translational species, so their combined thermal energy is

\frac{3}{2} RT (1 + ζ)

ζ N_{A} E_{I}

. Thus

U = \frac{3}{2} RT (1 + ζ) + ζ N_{A} E_{I} = \frac{3}{2} RT (1 + ζ) + ζ \frac{E _{I}}{k _{B} T} RT .

Radiation, excited states and nonideal interactions have been excluded consistently with the elementary Saha ionization equation.

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