Consider a system of N free electrons within a volume V. Even at absolute zero, such a system exerts a pressure P on its surroundings due to the motion of the electrons. To calculate this pressure, imagine that the volume increases by a small amount dV. The electrons will do an amount of work PdV on their surroundings, which means that the total energy Erot of the electrons will change by an amount dEtot = -PdV. Hence P = -dErot/dV. a) Show that the pressure of the electrons at absolute zero is 2 N P ==EFo, where Ero denotes the Fermi energy at absolute zero. b) Calculate Efo and P for solid copper, which has a free-electron concentration of 8.45 x 1028 m-3. Express Ero and P in electronvolts and atmospheres, respectively. c) The pressure you found in part (b) is extremely high. Why, then, don't the electrons in a piece of copper simply explode out of the metal?

Consider a system of N free electrons within a volume V. Even at absolute zero, such a system exerts a pressure P on its surroundings due to the motion of the electrons. To calculate this pressure, imagine that the volume increases by a small amount dV. The electrons will do an amount of work PdV on their surroundings, which means that the total energy Erot of the electrons will change by an amount dEtot = -PdV. Hence P = -dErot/dV. a) Show that the pressure of the electrons at absolute zero is 2 N P ==EFo, where Ero denotes the Fermi energy at absolute zero. b) Calculate Efo and P for solid copper, which has a free-electron concentration of 8.45 x 1028 m-3. Express Ero and P in electronvolts and atmospheres, respectively. c) The pressure you found in part (b) is extremely high. Why, then, don't the electrons in a piece of copper simply explode out of the metal?