課程名稱︰普通物理學甲上
課程性質︰必修
課程教師︰林敏聰老師
開課系所︰電機系
考試時間︰無限
試題 :Total: 100%
1. Please write down the three laws of thermodynamics with brief interpretation. (15%)
2. Please prove the relation, pV^γ= 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%)
3. (a) Please derive the entropy change: ΔS = S_f – S_i
= n R ln( V_f / V_i ) + n Cv ln( T_f / T_i ) for all reversible process that take the gas from state i to state f.
(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.
(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).
(You can use the Stirling's Approximation: ln N! = N ln N - N .)(25%)
4. (10%) Please express (in bulk modulus B and gas density ρ) and derive the equation for the sound wave speed v in air from Newton's second law. (10%)
5. One mole of an ideal gas are expanded from V_1 to V_2 = 3 V_1. 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%)
6. 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. (10%)
7. What phase difference between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 1.50 times that of the common amplitude of the two combining waves? Express your answer in (a) degree (b) radians (c) wavelengths. (15%)
8. Good luck!!! Happy NEW YEAR!
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