課程名稱︰普通物理學甲上
課程性質︰系必修
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）︰2008/01/19
考試時限（分鐘）：無限
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. (a) (10%) Please write down the three laws of thermodynamics with a brief
interpretation.
(b) (5%) Please give two examples which one may explain by using the
concept of entropy. Please give the difinition of the entropy before doing
that.
2. (5%) What is the definition of thermodynamic process? Is a free expansion
a thermodynamic process? Why?
3. (a) (5%) Please derive the entropy change: ΔS = Sf - Si = nR×ln(Vf / Vi) +
nCv×ln(Tf / Ti) for all reversible processes that the gas from state i to
state f.
(b) (5%) May one use this ralation to calculate the change in the entropy
for a free expansion process V to 2V? How? And why?
(c) (10%) Derive this increase of entropy with statistical mechanics (using
the Boltsmann's entropy equation S = k×lnW, where k is the Boltzmann's
constant, W is the multiplicity of the cofiguration). Before doing this,
please explain what are microstates and configurations, respectively.
4. (10%) Consider thr ideal gas in a Carnot cycle, the heat QH transferred
from TH thermal reservoir into this cycle and the heat QL transferred from
this cycle to the TL thermal reservoir. During the adiabatic processes,
show that P(V^γ) = constant, where γ = Cp / Cv, and that efficiency of
this Carnot cycle can be written as η = 1 － QL / QH = 1 － TL / TH.
5. (15%) A pipe with length L is closed in one end and filled with gas. A
speaker is just outside the pipe to send sound wave into the pipe.
(a) Show that the speed of sound wave in the elastic medium is sqrt(B / ρ)
(B: bulk module, ρ: mass density)
(b) Use (a) to show that the speed of sound in the air is sqrt(γRT / M).
(M: average air mass per mole, γ: adiabatic constant,
R: ideal gas constant, T: absolute temperature)
(c) If the amplitude of the speaker is doubled, how much is the sound level
increased?(in dB)
6. (5%) 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?
7. (10%) An ideal gas in a container separated into two parts by a slab. Each
part has the pressure P and molecule number N, but their temperatures are
T1, T2 and volume are V1 and V2, respectively. Now take the slab away, when
the ideal gas reaches thermal equilibrium. What is the entropy change of
this system?
8. (10%) Consider one object isolated in vacuum chamber. Only two wires are
connected to that object to give an average heating power of P Watt. What
will be the equilibrium temperature of that object, if the wire each has
radius r, length l, and thermal conductivity σ, and the chamber is kept
at room temperature? Take that object as ideal black body and has
effective surface area of A.
9. (10%) The internal energy of a van der Waals gas is U = (3/2)nRT + an^2/V +
constant.
(a) Find Cp as a function of V and T.
(b) Find Cv as a function of V and T.
(c) What is the value of the parameter γ = Cp / Cv for this game?
Check that your result reduces properly in the low density limit.
10. Good Luck and Happy New Year!!!
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