課程名稱︰普通物理學甲上
課程性質︰大一必修
課程教師︰林敏聰
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰2007.1.11
考試時限（分鐘）：不限
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(10%)Please write down the three laws of thermodynamics with a brief
interpretation.
2.(a)Derive the entropy chang:ΔS=Sf-Si=nRln(Vf/Vi)+nCvln(Tf/Ti) for all
reversible processes that take the ideal gas from state i to state f.(5%)
(b)May one use this relation to calculate the change in the entropy for a
free expansion process from V to 2V?How?And why?(5%)
(c)Derive this increase of entropy with statistical mechanics(using the
Boltsmann's entropy S=klnW,where k is the Boltsmann's constant,W the
multiplicity of the confriguration).Before doing this,please give explain
what are microstates and configuration,respectively.(10%)
(Hint:lnN!=N(lnN)-N,while N is large)
3.(10%)Construct plots of P versus V,T versus S,and S versus Eint of ideal gas
for the adiabatic expansion thermodynamic process.(Please point out the
initial and final state on your curve.)
4.(10%)What is the entropy change (a)for any reversible CLOSED cycle and (b)
for the irreversible process whose final T and V are the same as the initial
ones.Why?
5.(10%)For adiabatic processes in an ideal gas,show that(a)the bulk modulus is
given by dp
B=-V———=γP
dV _______ _______
And therefore(b)the speed of the sound in the gas is v=√γp/ρ =√γRT/M
6.(10%)Please express(in string tension τ and mass length densityμ)and
derive the equation for the wave speed v on stretched string from Newton's
second law.
7.(10%)The pressure in a certain ultra-high vacuum chamber is 1.0x10^(-10)mbar.
(a)Derive the expression for mean free path,and what is the mean free path
for the residual gas molecules at room temperature(300K),given the average
molecule diameter 2.0x10^(-10)m?
(b)Assuming a very cold metal plate such that every molecule colliding the
plate will stick to it,how long will it take to cover the plate with one
mono-layer of molecule,given one mono-layer contains 1.0x10^19 molecules/m^2?
(1mbar=100Pa)
8.(10%)(a)Please derive the general Doppler effect equation.Assume the motion
of source and detector is collinear,and let the speed of sound,detector,and
source is V,Vd and Vs,respectively.
(b)Shown in figure1,a radar gun is behind a pitcher to detect the ball speed.
Assume the source frequency,detected frequency,and sound speed is fs,fr,and v
,respectively.What is the speed of the ball?
9.(10%)Figure2 shows that,in cross section,a solid sphere of radius R3 is
concentric with a spherical shell of inner radius R2 and outer radius R1.The
temperature corresponding to each interface is also shown in the figure.
Assume in a steady-state process,T1>Tx>T3,and T1 and T3 are maintained by
thermal reservoir.
(a)What is the conducting rate(the amount of energy transferred per unit time
)between T1 and Tx?The thermal conductivity of spherical shell is K.
(b)Assume the solid sphere and the spherical shell are blackbodies,and the
temperature difference of T1 and Tx is small such that thermal radiation
within the shell can be neglect.Find out the equation that can be used to
solve Tx.
10.Good luck!!!Happy NEW YEAR!
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