9:03 AM PP. MUSIC 2010. with respect to CACHING Caper pre vide a full confirmation of the third law. PROBLEMS 10-1 Show that the heat capacity at constant volume can be written Cy as a In T It follows that as 70, In T- and S-0, so that Cy-0, in confirmation of Equation (10.18). By the same argument, Cp 0 as T0. 180 Chap. 10 The Third Law of Thermodynamics 10-2 Show that. in view of the third law. neither the ideal gas equation nor the van der Waals equation can hold at 7 = 0. 10-3 (a) Show that the third law cannot predict the value of the isothermal com- pressibility at absolute zero. (It remains finite.) (b) The isothermal bulk modulus B is the reciprocal of K. B = - av Show that aB lim = 0. dT 10-4 According to Debye's theory of heat capacities, to be discussed in Chapter 16. the specific heat capacity of an insulating solid at very low temperatures is given by C 12 TR T where c, is in the usual units of J kilomole 'K. Find the specific entropy of such a solid at 7 = 0.01K and 7 = 10K, given that = 300K. 10-5 (a) Show that if C = b7 at low temperatures. the third law requires that a > 0. (b) If CaTbT at low temperatures, calculate the variation of the entropy with temperature. 10-6 Consider a solid whose equation of state is PV - f(V) = AU. where f (V) is a function of the volume only and A is a constant. Show that Cy0 as 7-0. 10-7 A low-temperature physicist wishes to publish his experimental result that the heat capacity of a nonmagnetic dielectric material between 0.05K and 0.5K varies as AT2+BT3. As editor of the journal. should you accept the paper for publication?