[試題] 109-1 蔡政達 熱物理 期末考
課程名稱︰熱物理
課程性質︰物理系必修
課程教師︰蔡政達
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰2021/01/12
考試時限（分鐘）：110分鐘
試題 :
1. Using the fact that dv/v is an exact differential, prove that
∂ß ∂κ
(----) = - (----) . [20 points]
∂P T ∂T P
2. The gibbs function of a certain gas is
CP^2 DP^3
G = nRT ln(P) + A + BP + ----- + ---- ,
2 3
where A, B, C, and D are constants. Find the equation of state of the gas.
[20 points]
3. Show that for a closed system consisting of two phases coexisting in equil-
ibrium at a temperature T and under a pressure P,
∂P T dP 2
(----) = - --- (---). [20 points]
∂V s C_v dT
Here dP/dT is the slope of the phase equilibrium curve.
4. Show that, during a first-order phase transition:
(a) The change of entropy of the system undergoing the transition is a
linear function of the volume change. [10 points]
(b) The change of internal energy is given by
d(ln(T))
ΔU = L(1 - ---------) . [10 points]
d(ln(P))
5. Show that, in view of the third law, neither the ideal gs equation nor
the van der Waals equation can hold at T=0. [20 points]
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心得：今年冬天好冷
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※ 編輯: fafeiwen (140.112.102.241 臺灣), 01/12/2021 17:18:35