Consider N electrons (of mass m) within a metal of volume V,...

Consider N electrons (of mass m) within a metal of volume V, at absolute zero. (a) Show that the average energy of the electrons is $3E_F/5$, where $E_F$ is the Fermi energy. (b) Explain why $dU = -pdV$. (c) Using (b), find the pressure exerted by the electrons at absolute zero.

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Hi, this is a statistical mechanics (Thermodynamics) question and is the third time I am posting this. I have reported the other two as they were literally word-for-word chat GPT and AI answer generated and were wrong. If you choose to answer this make sure it makes sense to you and that you write out the equations and solution along with the explanation clearly. In the past some of the answers I have gotten were handwritten, if that's easier please do so as it honestly makes more sense. Please answer this question using your knowledge of the subject and don't use AI to cheat your way though as I can do that myself and would not be paying for Chegg if the AI was right. UPLOAD A HANDWRITTEN SOLUTION I HAVE REPORTED THE PAST 5 ANSWERS ON DIFFERENT QUESTIONS AND FROM THE ONES THAT I HAVE RECEIVED THE EXPERT ANSWERS HAVE BEEN REMOVED FOR PLAGIARISM. If you are going to use AI make sure its correct and clear don't use AI though because I pay for chegg and the AI IS WRONG. Consider N electrons (of mass m) within a metal of volume V, at absolute zero. e Show that the average energy of the electrons is 3EF/5, where EF is the Fermi energy. b) Explain why dU = -pdV. Using (b), find the pressure exerted by the electrons at absolute zero.

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Consider N electrons (of mass m) within a metal of volume V, at absolute zero. (a) Show that the average energy of the electrons is $3E_F/5$, where $E_F$ is the Fermi energy. (b) Explain why $dU = -pdV$. (c) Using (b), find the pressure exerted by the electrons at absolute zero.

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