課程名稱︰物理化學一
課程性質︰化學系必修
課程教師︰林萬寅
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰96年四月14日
考試時限（分鐘）：四小時
是否需發放獎勵金： 是
試題 :
1. (10％)
The Second and third virial coefficients( in the expansion of Z in power of
1/Vm) for argon at 300 K ae B=-0.022 L/mol and C=1.2x10^-3 L^2/mol^2.
Assuming that the ideal gas law holds sufficiently well for the estimation
of the second and third terms of the expansion,calculate the compression
factor(Z) of Ar at 100 atm and 300K and estimate its molar colume under
these conditions.
2. (15%)
The compression factor of a certain gas is given by Z=1+(-B/Vm + C/Vm^2)/RT
where B and C are constants. Find the critical constants
Pc, Vc, Tc of the gas in terms of B and C.
3. (10%)
A perfect gas was allowed to expand resersibly and adiabatically to twice
its colume; as a result the terperature fell from 300 K to 240 K and its
presure fell from 1.0 atm to 0.4 atm. Evalute Cp of the gas
4. (10%)
A gas obeys the equation of sate Vm = RT/P +aT^2 and its Cp,m is given by
A＋BT＋CP, where a, A, B and C are constants. Find the expression of the
Joule-Thomson coefficient μ=(dH/dP)h (d是偏微分)
5.(10%)
a. If h is the height above sea level, show that the decrease in atmosphere
due to a rise dh is given by: dP/P=-Mg/RT x dh. Where M is the average
molar mass of air. Assume ideal gas behavior.
b. Show that the decrease in pressure in an adiabatic reversible expansion
of an ideal gas is given by:
dP/P = γ/γ-1 x dT/T
where γ=Cp/Cv
c. If the decrease in pressure in (a) is due to the adiabatic expansion of
air. Estimate the decrease in terperature per 100m of rise (γ=1.4)
6. (10%)
A certain gas obeys the equationof state Vm = RT/P + ( b-a/RT ), where
a and b are constants. Show that the Boyle temperature of the gas is given
by Tb= a/Rb, and the inversion temperature is given by Ti = 2a/Rb
7. (10%)
A piston exerting a pressure of 1.9 atm rests on the surface of water at
373 K . Te pressure is reduced infinitesimally, and as a result 9.0 g of
water ebaporates and absorbs 20.5 kJ of heat. Calculate w, ΔU, and ΔH.
Assume the conpression factor of water capor is given by
Z= 1+B/Vm, where B = -1.2L/mol at 373K
8. (10%)
Assume that helium obeys the van der Waals equation of state.
(a) Show that the Joule coefficient of helium is given by
η= (dT/dV)u = - a/CvVm^2
(b) Determine the change in temperature when one mole of helium gas
undergoes a Joule expansion from 0.5 L to 5.0 L
( a=0.034 atmL^2/mol^2, b=0.0234 L/mol,Cv = 1.5 R )
9. Fig 1. shows an adiabatic container with a movable piston . One mole of
the sameideal gas (Cv,m = 2R for all temperatures) at the indicated
conditions is enclosed in each side of the pistion. By means of a heater,
heat is supplied slowly to the gas on the left-hand side.
It expands and compress the gas on the right-hand side until its pressure
has increased to 27 atm
(a) Find q, w ΔU, ΔH and the final temperature on the right side.
(b) Find q, w ΔU, ΔH and the final temperature on the left side.
(Hint; the right hand side is compressed reversibly and adiabatically)
Fig 1
┌────────────────────────────┐
│ │
│ ┌─┐───┌────┐─┌──────────┐ │
│ │ │heater│ ▕ p▕ │ │
│ │ └───┘ ▕ i▕ 1 mole │ │
│ │ 1mole ▕ s▕ 8 atm │ │
│ │ 8 atm ▕ t▕ Vo │ │
│ │ Vo ▕ o▕ 300K │ │
│ │ 300K ▕ n▕ │ │
│ │ ▕ ▕ │ │
│ └──────────┘═└──────────┘ │
│ │
└────────────────────────────┘
│
│
│
│
│
│
│
│
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│
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