課程名稱︰熱物理學
課程性質︰必修
課程教師︰王名儒
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰96/1/19
考試時限（分鐘）：150分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.
Write down the differential forms of the following four thermal dynamic
potentials: dU (internal energy), dH (enthalpy), dA (Helmholtz function),
and dG (Gibbs function), in terms of the thermal dynamic functions P, V,
S or T in combination with their proper differentials (5 pt.). Write down
the four Maxwell relations from above formula (5 pt.). Derive the three
TdS equations, namely, TdS = CvdT + Tβ/κdV, TdS = CpdT - TVβdP and
TdS = Cp/(βV)dV + Cvκ/β dP, where β is the volume expansivity and κ
is the isothermal compressibility (15 pt.).
2.
Please draw the PVT equilibrium surface for one mole of H2O (5 pt.) and
draw its phase diagram (i.e., P-T projections of different phases. The
solid region, liquid region, vapor region, gaseous region, fusion curve,
vaporization curve, sublimation curve, triple point and critical point
should be labeled (5 pt.). Derive the Clausius-Clapeyron equation,
dP/dT = (s2-s1)/(v2-v1), for first-order phase-transition curves on the
phase diagram, where 1 and 2 denote different phases (15 pt.).
3.
Show that the change of entropy in a mixing process of two different ideal
gases is ΔS=-nR(x1lnx1 + x2lnx2), where x1 and x2 are the mole fractions
of the two gases. Before the partition is removed, there are N1 particles
of the same kind in one side and N2 particles of another kind in the other
side with the same temperature and pressure. You can derive this with
classical method (10 pt.) and statistical method (15 pt.).
4.
In an osmotic pressure apparatus, let the pressure of the pure solvent be P0
and that of the dilute solution be P, the temperature being T throughout the
system. The molar Gibbs function of the pure solvent is g". (a) Show that,
at equilibrium, g"(T,P0) = g"(T,P) + RTln(1-x), where x is the mole-fraction
of the solute. You need to show the chemical potential μ=g+RTlnx first,
using a gas/fluid mixing process (10 pt.). (b)For an infinitesimal change of
x at constant T, show that v"dP + RTd[ln(1-x)] = 0, assuming the pure
solvent side has a much wider area than that of the dilute solution side (10 pt.). (c) Integrating P from P0 to P, and x from 0 to x, show that Πv"
pt.). (c) Integration P from P0 to P, and x from 0 to x, show that Πv"=xRT,
where Π=P-P0. Compare this equation with the ideal-gas law (5 pt.)
5.
Describe the goal, the setup, the procedure and the important points of any
experiments introduced in this course (extra points).
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