In the lecture we derived an expression for the heat capacity of a 3-dimensional solid. Derive a) 1 mark] Work out the...
In the lecture we derived an expression for the heat capacity of a 3-dimensional solid. Derive a) 1 mark] Work out the density of modes in terms of wavenumber k, ie g(k)dk. b) [1 mark] Work out the density of modes in frequency space, g(w)dw. c) 12 marks] Work out the 2D Debye frequency W2 and temperature 62D in terms of the areal density PA-L2. d) [2 marks] Derive an exact expression for the total energy of vibrations U in the lattice. e) [2 marks] Derive an expression for the low-temperature limit of the heat capacity. Express your answer in terms of the 2D Debye temperature, 2D. Hint: Joo etdr-2((3) ^ะ 2.404, where is the Riemann Zeta function f) [2 marks] Derive an expression for the high-temperature limit of the heat capacity. Can the result be explained by the
In the lecture we derived an expression for the heat capacity of a 3-dimensional solid. Derive a) 1 mark] Work out the density of modes in terms of wavenumber k, ie g(k)dk. b) [1 mark] Work out the density of modes in frequency space, g(w)dw. c) 12 marks] Work out the 2D Debye frequency W2 and temperature 62D in terms of the areal density PA-L2. d) [2 marks] Derive an exact expression for the total energy of vibrations U in the lattice. e) [2 marks] Derive an expression for the low-temperature limit of the heat capacity. Express your answer in terms of the 2D Debye temperature, 2D. Hint: Joo etdr-2((3) ^ะ 2.404, where is the Riemann Zeta function f) [2 marks] Derive an expression for the high-temperature limit of the heat capacity. Can the result be explained by the