Tiêu đề Free electron theory and Sommerfeld Model Study Material .pdf ✅

University College of Science, Tumkur 4 Let n be the conduction electron per unit volume of the conductor and v be the average velocity of these electrons. According to classical theory, the average kinetic energy of free electron at temperature T is 1 2 mv 2 = 3 2 kBT Therefore, at end A, average kinetic energy of an electron = 3 2 kBT At B, average kinetic energy of the electron = 3 2 kB(T − λ dT dx ) Therefore, the energy carried by an electron from end A to end B is E = 3 2 kBT − 3 2 kB(T − λ dT dx) i.e. E = 3 2 kBλ dT dx (1) Let n is number of free electrons per unit volume of the conductor. The electron can move along 6 different directions (say +x, −x, +y, −y, +z, −z directions) with equal probabilities. Then number of free electrons moving along each direction is 1 6 n And the number of electrons moving from A to B per unit area per unit time is 1 6 nv Therefore, amount of heat energy carried by electrons per unit area per unit time from A to B is (or in one direction) QAB = 1 6 nv × 3 2 kBλ dT dx QAB = 1 4 nvkBλ dT dx Similarly, heat energy carried from B to A is per unit area per unit time is QBA = − 1 4 nvkBλ dT dx Therefore, the net amount of heat energy transferred between end A and end B is