2. A system consists of N very weakly interacting particles at a temperature T high enough...
2. A system consists of N very weakly interacting particles at a temperature T high enough that classical statistical mechanics is applicable. Each particle is fixed in space, has mass m, a. Calculate the heat capacity of this system of particles at this temperature in each of the i. The effective restoring force has magnitude κ x, where x is the displacement from and is free to perform one-dimensional oscillations about its equilibrium position. following cases: equilibrium. The effective restoring force has magnitude Kx3 ii. You may proceed by first writing down an expression for the single particle partition function with the energy being E pi/2m + V(x), where p is a particular value of the momentum and x is a particular value of the displacement from equilibrium, such that Because you are in the classical regime, p and x are continuous variables and you should therefore convert this sum to an integral over p and x (what are the limits of integration?). From that, calculate Z and then U b. At room temperature the resistivity p of a metal is proportional to the probability that an electron is scattered by the vibrating atoms in the crystal lattice. This probability is proportional to the mean square amplitude of vibration of the atoms. Assuming classical statistical mechanics to be valid in this temperature range, what is the dependence of the electrical resistivity on the absolute temperature?