Calculations for bismuth of consequences of nonlinearities in the theory of second sound

Abstract

The relation τ( θ) q 1 + q = − κ( θ) θ, in which q is the heat flux, θ the temperature θ x = ∂θ/ t6 x, q 1 = ∂/ ∂t, is often used to describe second sound in solids. Compatibility of the relation with thermodynamics requires that the internal energy density e depend not only on θ but also on q, i.e. that e = e n ( θ) + a( θ) q 2 with 2a(θ) = −θ 2 d[τ(θ) κ(θ) −1θ −2] dθ . This quadratic nonlinearity in q imply a dependence of the speed of heat pulses on heat flux and influences the growth of singularities in derivatives of θ. Available data for pure crystals of bismuth at temperatures below that at which the steady-state thermal conductivity has its maximum value are employed here to improve previous estimates of the magnitude of such effects.