Exchange of energy between diatomic gas molecules and a solid surface

Abstract

When gas molecules are incident on a solid the exchange of energy may be measured by Knudsen’s accommodation coefficient. If the gas molecules before collision have a mean energy corresponding to the temperature T 2 and the solid surface is at temperature T 1 , then the gas molecules after collision will have a mean energy corresponding to a temperature T´ 2 , T´ 2 being a function T 1 and T 2 . The accommodation coefficient α is then defined as α = Lt T1 → T 2 (T´ 2 ─ T 2 )/(T 1 ─ T 2 ). Hitherto* it has only been possible to develop a theory for monatomic gases, the atoms of which possess translational energy alone. This paper is an attempt to include the effects which must arise from the rotation of diatomic molecules. The first step in the calculation of the accommodation coefficient is to obtain the probability p (Wr; nm | n 1 m 1 ) that when a gas molecule with transitional energy W r and rotational energy corresponding to the quantum state m collides with a solid atom in quantum state n , a transition will take place to the state specified by the quantum numbers n 1 and m 1 , the balance of energy being taken up by the translational motion of the molecule. The accommodation coefficient α is then found by averaging p (Wr; nm | n 1 m 1 ) over all accessible values of W r , n , m , n 1 , m 1 , with the proper weighting factors.