2. Heat Capacity. a. The dispersion relation for a surface (2D) tension waves on a liquid of density and surface tension o is given below. w? = k'o/e a. Using this relation, construct a Debye Theory to show how Ctension scales with temperature. 2 = b. Using kinetic theory of gases, show how K (thermal conductivity) scales with temperature at high and low temperatures. Plot your anticipated temperature dependence and compare this temperature dependence to that of graphite. c. Now, assume that the liquid has finite number of contaminants (impurities / defects), how would the thermal conductivity change? Justify your answer and plot pure vs contaminated cases