課程名稱︰統計物理(一) Statistical Physics(I) 課程性質︰必修／物理研究所；選修／天文物理所、應用物理所 課程教師︰蔡政達 開課學院：理學院 開課系所︰物理研究所、天文物理所、應用物理所 考試日期（年月日）︰2018年5月14日 考試時限（分鐘）：120分鐘 試題 : Statistical Physics(I) Midterm Examination(2) 1.[20 points]Show that, for a classical ideal gas, S Q_1 ╭ \partial ln Q_1 ╮ ── = ln── + T│ ──────── │ Nk N ╰ \partial T ╯P. 2.[20 points]Determine the work done on a gas and the amount of heat absorbed by it during a compression from volume V_1 to volume V_2, following yhe law PV^n = const. 3.[20 points]Show that the entropy of a system in the grand canonical ensemble can be written as S = -k Σ P_{r,s} ln P_{r,s}, r,s where P_{r,s} is given by exp(-αN_r - βE_s) P_{r,s} = ─────────── . Σ exp(-αN_r - βE_s) r,s 4.[20 points]In the thermodynamics limit (when the extensive properties become infinitely large, while the intensive ones remain constant), the q-potential of the system may be calculated by taking only the largest term in the sum ∞ Σ Z^{N_r} Q_{N_r}(V,T) . N_r = 0 Verify this statement and interpret the result physically. 5.[20 points]Show that expression U-A ╭ \partial q ╮ S = ─── = kT │ ───── │ - Nk lnz + kq T ╰ \partial T ╯z,V for the entropy of a system in the grand canonical ensemble can also be written as ╭ \partial ╮ S = k │ ───── (Tq) │ . ╰ \partial T ╯μ,V --

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