Question 2 [30 points): The pressure is given by the derivative of the internal energy with respeet to volume. P = _EJ_L:. 31' a} Use this equation to derive the relation between the pressure and volume of the free eleetron gas at El K. b} The bulk modulus of a material is a measure of its elasticity with respect to a uniform compression and is given by B = 4.7% . Show that the bulk modulus of an electron gas . . 2 at D K 1s given by B = g HEF' e} Use this equation to evaluate the bulk modulus of potassium (K) and compare with the experimental value of 3.?x109 333mg. The electron density in potassium is 1.4x1323 m'3