推 lateas:出現了 01/22 00:35
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）︰2008/1/15
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. The specific Gibbs free energy for a gas is given by g=RTln(P/P0)-AP, where
A is a function of T only and P0 is a constant. Find the expressions for
the following quantities:(a) the equation of state (5 points);(b) the
specific entropy (5 points) (c) the specific Helmholtz free energy
(5 points) (d) the constant pressure specific heat capacity Cp (5 points)
2. Please draw the phase diagram (i.e. P-T projections of different phases)
of H2O. The solid region, liquid region, vapor region, gaseous region,
fusion curve, vaporization curve, sublimation curve, triple point and
critical should be labeled (5 points). Derive the Clausius-Clapeyron
equation, dP/dT=(s2-s1)/(v2-v1), which describes the first-order
phase-transition curves on the phase diagram, where 1 and 2 denote different
phases (10 points). Use this equation and the assumption of ideal gas to
find the functional form of the vaporization curve (5 points). Show that the
obtained result is a good approximation to the saturated vapor pressure at
fixed T, where other gas milecules are also presented in the atmosphere
(10 points). You need to show the chemical potential of vapor first,
μ=g+RTlnx using an ideal gas mixing process where x is the mole-fraction of
H2O in the gas state and g is the specific Gibbs free energy for pure H2O
vapor without any other mixing components (10 points)
3. Derive the following equation for the incident flux Φ=1/4 nv of an ideal
gas, where n is the number density and v is the average speed of the gas,
assuming a uniform and isotropic condition (10 points). Show that the
equation of state of the photon gas is PV=1/3 U where U is the total energy
of state of the photons (10 points)
4. Derive the Bose-Einstein distribution for an isolated system consisting of
one ideal Bose gas. The energy level εi and the degeneracy of the energy
state, gi are assumed to be known. The total number of particles,N, and the
total energy,E, are conserved. You need to use the Largrange multiplier
method in order to derive the B.E. distribution at thermal equilibrium.
Note that you don't need to find out the two Largrange multipliers in the
derivation but you need to argue their physical meanings using a dilute gas
limit (20 points)
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