[考試] 普物期末考考古題（林敏聰）13.Jan.2002

[Steggie (p2新板Tread_softly)]

林敏聰普物考古題連載開跑 XD
總共有三份，敬請期待。
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上次打半天，結果因為離奇的 ptt 當機而付諸流水 orz
（連暫存檔也不給我 >"<）
今天終於鼓起勇氣再重打了一次 |o/
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怎樣快速 print 下來呢？
在看板裡面按大 F 寄回自己的 e-mail 信箱吧 ^^
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這一份還有一些 Rolling 和 Oscillation 的題目，應該是當年進度不同所致。

Total: 150% 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. (5%)

3. A solid cylinder is attached to a horizontal massless spring so that it can
   roll without slipping along a horizontal surface (Fig.1) The spring
   constant k is 3.0 N/m. If the system is released from rest at a position in
   which the spring is stretched by 0.25m, find (a) the translational kinetic
   energy and (b) the rotational kinetic energy of the cylinder as it passes
   through the equilibrium position. (c) Show that under these conditions the
   center of mass of the cylinder executes simple harmonic motion. What is its
   period? (15%)

   Fig.1
          | k  M ←╮（逆時鐘方向）
          |~~~~⊙  

4. (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 2V. 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 .)

5. 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%)

6. 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? (15%)

7. Please construct the plots of P versus V, T versus S, and S versus
   Einternal（internal 下標）for the isothermal expansion and isobaric
   expansion thermodynamic process. (15%)

8. One mole of an ideal gas are expanded from V1 to V2 = 3 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%)

9. 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%)

10. (10%) Consider a damped simple harmonic motion with the total force
   ΣF = - kx - bv, where k is force constant of the spring, x the
   displacement, v the velocity, b the damping constant. Please write down
   and solve the (differential) equation of motion from the Newton's second
   law.

11. Good luck!!! and Happy NEW YEAR!

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※ 編輯: Steggie         來自: 211.75.136.1         (12/14 08:45)
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