Consider a system of N free electrons within a volume V.

Chapter 42, Problem 42.53

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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 p dV on their surroundings, which means that the total energy Etot of the electrons will change by an amount dEtot = -p dV. Hence p = -dEtot>dV. (a) Show that the pressure of the electrons at absolute zero is p = 32>3 p4>3 U2 5m a N V b 5>3 (b) Evaluate this pressure for copper, which has a freeelectron concentration of 8.45 * 1028 m-3 . Express your result in pascals and in atmospheres. (c) The pressure you found in part (b) is extremely high. Why, then, dont the electrons in a piece of copper simply explode out of the metal?

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