Thermodynamic Identity - Solid State Physics - Solved Paper, Exams of Solid State Physics

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NAME: Physics 112 Spring 2004 Midterm1 CSoudtzon) Monday 23 February 2004, 8:10-9:00 a.m. 50 points=S0minutes 1) Thermodynamic identity (5 points) Write down the thermodynamic identity*(i.e. the full differential with the appropriate macroscopic thermodynamic variables) for the energy U and the free energy F=U-to. al) = tdo— pdV + sudd) = qs —pdV tidal dh = ~ode. —pelV-tardat = — Sot —pelV tarels/ What the natural independent variables to use with U and F? U=UGVA), fe Pov, x) 2) Temperature, pressure and chemical potential of an ideal gas (15 points) Consider an ideal gas of indistinguishable N spinless particles in a volume V and total energy U. Using our prescription of the number of spatial quantum states per unit phase space volume, integrating in momentum space on the hypersphere where the total energy is U, and keeping carefully track of the numerical coefficients, we can compute the number of states and therefore the entropy at equilibrium. For large N l,m 2?) ov OU.VAN) = Nos) 5525) tN longs +52) Calculate. a) (5 points) the temperature of the ideal gas we consider {. _? * > BA =* Slav = Sy} ag rn Je BG ° 2 o UF 34) What is the average kinetic energy per molecule? u 3 2 eo ts frm Y= Sat Us Ki oe —__