課程名稱︰普通物理學甲上 課程性質︰物理系必帶 課程教師︰邱雅萍 開課學院：理學院 開課系所︰物理學系 考試日期（年月日）︰2019/01/08 考試時限（分鐘）：100分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : General Physics -- Final Exam 2019/01/08 (10:20-13:00) 1.(5%)[Fluid] Identify that Bernoulli's equation is a statement of the conser- vation of energy. 2.(5%)[Wave] Prove the general differential equation that governs the travel of all types is ∂^2 y 1 ∂^2 y ------ = --- -------- ∂x^2 v^2 ∂t^2 3.(10%)[Sound] Tuning Forks Resonace & Beat Frequency: From the video, you see the demonstration of the Resonance and Beat Frequency. (a)Explain what is the definition of the beat frequency and (b)derive the value of the beat frequency? Set the two waves having frequencies, f1 and f2, respectively. 4.(20%)[Kinetic theory of gases] (a)Prove that the pressure exerted by n moles of an ideal gas is p=nMv^2_{rms}/(3V), where v_{rms}=((v^2)_{avg})^(1/2) is the root-mean-square speed of the molecules, M is the molar mass, V is the volume. (b)Prove the rms speed can be written in terms of temperature as v_{rms}=(3RT/M)^(1/2). Note that ∞ 9π ∫x^4e^(-ax^2)dx = (-----)^(1/2) 0 64a^5 5.(15%)[Thermodynamics Physics] Initially, 1 mole of oxygen (assumed to be an ideal gas) has temperature 310K and volume 12L. We will allow it to expand to volume 19L. (a)What would be the final temperature if the gas expands adiabatical- ly? Oxygen (O_2) is diatomic and here has rotation but no oscillation. (b)What would be the final temperature and pressure if, instead, the gas expands freely to the new volume, from an initial preesure of 2.0 Pa? 6.(10%)[Thermodynamic Physics] When n moles of an ideal gas double its volume in a free expansion (see Fig.1). What is the entropy change of the gas for this irreversible process? 7.(15%)[Thermodynamic Physics] Calculate the efficiency of the (idealized) Otto cycle. See Fig.2. 8.(20%)[Thermodynamic Physics] When a gas undergoes a process depicted as the straight line from a to c in Fig.3 the heat flow into the system is 180 J. (a)Find the work done from a to c. (b)If U_a=100J, find U_c. (c)What is the work done by the gas when it returns to a via b? (d)What is the heat transfer in the process cba? --

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