CALC Consider a system of N free electrons within a volume

Chapter 42, Problem 42.55

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CALC 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 of the electrons will change by an amount Hence (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 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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