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Thermal Radiation. Quantum Nature of Light.

Problem 5.250

Find the temperature of totally ionized hydrogen plasma of density \(\rho=0.10 \mathrm{~g} / \mathrm{cm}^{3}\) at which the thermal radiation pressure is equal to the gas kinetic pressure of the particles of plasma. Take into account that the thermal radiation pressure \(p=u / 3,\) where \(u\) is the space density of radiation energy, and at high tem peratures all substances obey the equation of state of an ideal gas.

Reveal Answer
T=3cRρ/σM3=2⋅107 K, where R is the universal gas constant, M is the molar mass of hydrogenT=\sqrt[3]{3 c R \rho / \sigma M}=2 \cdot 10^{7} \mathrm{~K}, \text { where } R \text { is the universal gas constant, M is the molar mass of hydrogen}
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