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Using band theory, explain how you can tell if a material is an insulator, conductor, or semiconductor. (PS: I'm not looking for "if it has a sea of electrons..." or "if it is a metal...") :)

Answer:|Assuming we're talking about a monatomic ideal gas, you can use Cv = 3/2R and Cp = Cv + R. These come by setting U=3/2nRT equal to Q=nCvT in an isovolumetric process. Going way back, the 3/2 comes from some pretty neat degrees of freedom stuff, but I'm not exactly sure how far I should be ...

Answer:|C. Temperature is constant during a phase change and is proportional to average kinetic energy of the particles.

This question was on an invitational test: and I am pretty confident though my answer was marked wrong. What do you think:

As a substance undergoes a change from the solid to ...

Consider a Carnot engine (an insulated cylinder with a piston filled with a gas). Why must the cylinder expand during the isothermal phase of the Carnot cycle in which heat flows into the cylinder from a heat source?