CALC When the pressure p on a material increases by an

Chapter 42, Problem 42.56

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CALC When the pressure p on a material increases by an amount the volume of the material will change from V to V + V, where is negative. The V bulk modulus B of the material is defined to be the ratio of the pressure change to the absolute value of the fractional volume change. The greater the bulk modulus, the greater the pressure increase required for a given fractional volume change, and the more incompressible the material (see Section 11.4). Since the bulk modulus can be written as In the limit that the pressure and volume changes are very small, this becomes (a) Use the result of 42.55 to show that the bulk modulus for a system of N free electrons in a volume V at low temperatures is (Hint: The quantity p in the expression is the external pressure on the system. Can you explain why this is equal to the internal pressure of the system itself, as found in 42.55?) (b) Evaluate the bulk modulus for the electrons in copper, which has a free-electron concentration of Express your result in pascals. (c) The actual bulk modulus of copper is Based on your result in part (b), what fraction of this is due to the free electrons in copper? (This result shows that the free electrons in a metal play a major role in making the metal resistant to compression.) What do you think is responsible for the remaining fraction of the bulk modulus?