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In this expression also the derivatives of the temperature are to be understood as average values. The similarity with the expression (2.22) for the radiative energy flux Frad = L(r)/(4nr2) is borne out if (2.22) is rewritten slightly,

Fr rad d Prad d T d T d r l (photons) c, where the radiation pressure Prad equals one-third the energy density of black-body radiation,

Prad= 1 aT 4, and where use has been made of the relation 4a = ac between Stefan's constant a and the radiation constant a to introduce the photon velocity c (velocity of light) as an analogy to the average speed of convective motion, vconv.

The radial bubble speed vconv may be estimated from the kinetic energy associated with the buoyant motion of the bubble. The average density deficiency is of the order

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