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 calcu1ate 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 E tot of the electrons will change by an amount dE tot = -pdV. Hence p = -dE tot /dV.(a) Show that the pressure of the electrons at absolute zero is(b) Evaluate this pressure for copper, which has a free-electron concentration of 8.45 x 1028 m-3. Express your result in Pascal??s and in atmospheres.(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 themetal?

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p= 32/3774/32 (N/5/3 *² (1) ³* 5m