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更正版！
Total: 150%（again XD）
1. Please write down the three laws of thermodynamics with brief
interpretation. (15%)
γ
2. Please prove the relation, pV = a constant, during an adiabatic process of
an ideal gas, where γ= Cp / Cv（p, v 下標）, the ratio of the molar
specific heats for the gas. (10%)
這題旁邊寫了個「必考」XD
3. (30%)
(a) Please derive the entropy change: ΔS = S - S（這邊沒有下標我想是 typo）
= n R ln( Vf / Vi ) + n Cv ln( Tf / Ti )（f, i, v 下標） for all
reversible process that take the gas from state i to state f. (10%)
(b) Please use this relation to calculate the change in the entropy for a
free expansion process from V to 4V. Please also give the reason that
you may do in this way. (10%)
(c) Derive this increase of entropy with statistical mechanics (using the
Boltzmann's entropy equation S = k ln W, where k is the Boltzmann's
constant, W the multiplicity of the configuration). (10%)
(You can use the Stirling's Approximation: ln N! = N ln N - N .)
4. Please express (in string tension τ and mass length density μ) and derive
the equation for the wave speed v on stretched string from Newton's second
law. (10%)
5. An apparatus that liquifies helium is in a room maintained at 300K. If the
helium in the apparatus is at 4.0K, what is the minimum ratio of the heat
delivered to the room to heat removed from the helium? (10%)
6. One mole of an ideal gas are expanded from V1 to V2 = 4 V1（1, 2 下標）. If
the expansion is isothermal at temperature 300K, find (a) the work done by
the expanding gas and (b) the change in its entropy. (c) If the expansion
is reversibly adiabatic instead of isothermal, what is the change of
entropy of the gas? (15%)
7. 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. (20%)
8. (10%) Please give a clear argument by using the concept of entropy to
explain that the heat will always flow from the high temperature to the low
temperature objects if there is no external work.
9. (20%) In an experiment, 200g of Al (with a specific heat of 900 J/kg．K）
at 373K is mixed with 50.0g of water at 293K with the mixture thermally
isolated. (a) What is the equilibrium temperature? What are the entropy
changes of (b) the Al, (c) the water, and (d) the Al-water system?
10. (20%) 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
γp γRT
v = sqrt( ── ) = sqrt( ─── )
ρ M
（sqrt 表示開根號 |||）
11. Good luck!!! Happy NEW YEAR!
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◆ From: 211.75.136.1
※ 編輯: Steggie 來自: 211.75.136.1 (01/03 07:48)