. Pressure and bulk modulus of an electron gas. (a) Derive a relation connecting the pressure and volume of an electron gas at 0 K. Hint: Use the result of Problem 1 and the relation between ep and electron concentration. The result may be written as p = (U/V). (b) Show that the bulk modulus B = -V(aplv) of an electron gas at 0K is B = 5p/3 = 10U/9V. (c) Estimate for potassium, using Table 1, the value of the electron gas contribution to B.