課程名稱︰物理化學
課程性質︰必修
課程教師︰金必耀
開課系所︰化學系
考試時間︰4/18/2006
試題 : (ρ請當成partial differential的symbol)
Problem 1. Thermal Expansivity 8%
For a liquid the cubic expansion coefficient α=(ρV/ρT)p / V is nearly
constant over a narrow range of temperature.Derive the expression for the
volume as a function of temperature and the limiting form for temperatures
close to To .
Problem 2. Exact and Inexact Differentials 8%
Show that
dq = dU + PdV = CvdT + RTdlnV
is not an exact differential,but
dq/T = CvdlnT + RdlnV
is an exact differential.
Problem 3. Entropy of heating 7%
By what amount is the entropy of 1 mole of water increased when the
temperature is raised from 0。C to 100。C at a constant pressure of 1 bar
Problem 4. Entropy of irreversible phase transition 7%
A thermostat at -10。C contains 1 mole of supercooled water at this
temperature at a pressure of 1 bar.By seeding with an ice crystal,the water
is caused to turn into ice at -10。C. How large is the entropy exchange
Problem 5. Adiabatic Expansion of an ideal gas 8%
Show that in a reversible adiabatic expansion of an ideal gas,the pressure and
volume are related by PV^γ=constant , where γ = Cp/Cv
Problem 6. Entropy of gases 9%
a) Derive the equation dH = TdS + VdP and show that ΔS for the change of one
mole of an ideal gas from (P1,T1) to (P2,T2) , assumong that Cp is
independent of temperature
b) How would the result change if instead of being temperature independent the
heat capacity could be written
c) Explain how the equation you derived in (a) depends on the gas being ideal
-i.e. what would be different for the general case
Problem 7. Volume dependence of Cv 6%
Determine the (ρCv/ρV)t for a van der waals gas.
Problem 8. Criteria for spontaneous change and equilibrium 5%
Prove the criteria for spontaneous change and equilibrium is dA≦0 at constant
T,V,and {Ni}
Problem 9. Fugacity of a real gas 10%
_
For a gas that follows the equation of state P(V-b)=RT , show that the
fugacity is given by
f = P*e^(bP/RT)
Problem 10. Equilibrium Conditions 9%
Shows that the conditions of two phases in thermal,mechanical and chemical
equilibrium are
a)T(α)=T(β)
b)P(α)=P(β)
c)μ(α)=μ(β)
Problem 11. Constant-temperature heat capacity 5%
Deriver
Cp = -(ρ^2 G/ρT^2)p
Problem 12. Legendre Transform and Maxwell Relation 10%
A one-component system has three natural variables , as is evident from
dU = TdS - PdV + μdn
a)How many different thermodynamic potentials can be constructed by making
Legendre transform ? Writing down the corresponding fundamental equation for
these thermodynamic potentials.
b)Show that
(ρμ/ρT)n = -(ρS/ρN)t
Problem 13. Residual Entropy 8%
Estimate the ice Ih residual entropy based on the Pauling's ice rule:
a)Each water molecule is oriented such that its two hydrogen atoms are
directed approximately toward two of the four surrounding oxygen atoms
(arranged almost in a tetrahedron)
b)Only one hydrogen atom is present on each O-O linkage
c)Each oxygen atom has two nearest neighboring hydrogen atomes such that the
water molecule structure is preserved
Explain your reasoning.
Thermodynamics has something to say about everything but does not tell us
everything about anything.
Martin Goldstein and Inge F.Goldstein, "The Refrigerator and the Universe"
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