課程名稱︰物理化學一-熱力學
課程性質︰必修
課程教師︰陸駿逸
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰2012/11/09
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.Carnot's theorem says that no engine working with two heat reservoirs (at
T_H, T_C)is more efficient than the Carnot engine. How does this lead to the
Clausius inequality Q_H/T_H + Q_C/T_C ≦0?
2.Derive the expression for (∂U/∂V)_T,n for a gas following the virial
equation with PV/nRT = 1 + nB/V.
3.At very low temperature, the conducting metal has the heat capacity
C_p(t) = aT + bT^3. Calculate its entropy S(T).
4.The nature uranium contains 0.7% of U-235. At room temperature, estimate the
minima work required to separate 0.007mole of pure U-235 from one mole
naturaluranium?
5.Derive the following relations:
(1) ╭ ∂H ╮ ╭ ∂G ╮
│───│ = │───│
╰ ∂P ╯S,n ╰ ∂P ╯T,n
(2) ╭ ∂S ╮ ╭ ∂V ╮
│── ─│ = -│───│
╰ ∂P ╯T,n ╰ ∂T ╯P,n
6.Given the following fundamentalrelation of a thermodynamics system
S = R(UV/n - n^3/UV)
where the notation follows the lecture. Calculate (1) the internal energy
U(T,V,n); (2) the equation of state P(T,V,n); (3) the Helmholtz free energy
A(T,V,n).
7.Suppose that a gas obeys
P = nRT/(V-nb) + an^2/(TV^2)
Calculate (∂C_v/∂V)_T,n.
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