Answer Happy

Problem 7.63 (Find the expressions of U and Cv at high and low temperatures for phonons in a 2D solid with area A. Sketch the Cv vs. T curve qualitatively. Specify the dependence of Cv on T at high and low temperatures.)
= Problem 7.63. Consider a two-dimensional solid, such as a stretched drumhead or a layer of mica or graphite. Find an expression in terms of an integral) for the thermal energy of a square chunk of this material of area A = L?, and evaluate the result approximately for very low and very high temperatures. Also find an expression for the heat capacity, and use a computer or a calculator to plot the heat capacity as a function of temperature. Assume that the material can only vibrate perpendicular to its own plane, i.e., that there is only one “polarization.”