課程名稱︰普通物理 課程性質︰化工系必帶 課程教師︰梁啟德 開課學院：理學院 開課系所︰ 考試日期（年月日）︰2016/1/14 考試時限（分鐘）：120分鐘 試題 : 1.Please prove that for an adiabatic expansion of an ideal gas, the pressure p and the volume V obey pV^γ=a constant, where γ=Cp/Cv is the ratio of the molar specific heats for the gsa. Cp isthe molar specific heat for a constant pressure process and Cv is the molar specific heat for a constant volume process, respectively(10%) 2.An elevator repairman(mass=73kg) sits on top of an elevator cabin of mass 655 kg inside a shaft in a skyscraper. A 61-m-long steel cable of mass 38 kg suspends the cabin. The man sends a signal to his colleague at the top of the elevator shaft by tapping the cable with his hammer. How long will it take for the wave pulse generated by the hammer to travel up the cable?(10%) 3.Determine the amplitude of the resultant wave when two sinusoidal string waves having the same frequency and traveling in the same direction are ocmbined, if their amplitudes are 6.0cm and 8.0 cm and they have phase constans of 0 and π/2 rad, repectively(10%).(Hint: use Phasors) 4.please prove that ∞ ∫ e^(-x^2)dx=√π/2 0 5.A satelltie is in a circular orbit around the Earth. The orbit has a radius of 3.75 times the radius of the Earth. What is the linear speed of the satellite?(10%). Hint: G=6.67x10^-11 m^3kg^(-1)s^(-2). The mass of the Earth is 5.97x10^24 kg. The radius of the Earth is 6.37x10^6 m. 6.If you squeeze the handle of a spray bottle(Fig.1), you cause air to flow horizontally across the opening of a tube that extends down into the liquid almost to the bottom of the bottle. If the air is moving at 50.0m/s, what is the pressure difference between the top of the tube ant the atmosphere? Assume that the densityof air is ρ=1.20 kg/m^3 [Hint: Use Bernoulli's equatioin for a negligible height difference. Before you squeeze the handle, the airflow speed is zero.] (10%) Figure 1 Spray bottle dor dispensing liquids in the form of a fine mist. http://imgur.com/a/3olrO 7.Please find the general solution of the following equation: d^2y dy ——-6—+9y=0 .(10%) dx^2 dx 8.Let us conside n moles of an ideal gas doubles its volume in a free expansion. Please use the Boltzmann's entropy equation S=klnW and Stirlings's approximatioin lnN!=N(lnN)-N when N(the number of ideal gas moleclues) is large to prove that Sf-Si=nRln2. [Hint:R is the gas constant, k=nR/N is the Bltzmann constant, and W is the number of microstates]. (10%). Please prove that if we use △S=∫dQ/T, the change of the entropy of an ideal gas doubles its volume in a free expansion is also given by Sf-Si=nRln2. (10%) 9.Imagine a Carnot engine that operates between the temperatures TH=850K and TL=300K. What is the efficiency of this engine? (10%) [Hint:fig.2] Figure 2 The P-V diagram of a Carnot Engine. http://imgur.com/ZZhogKI -- A census taker once tried to test me. I ate his liver with some fava beans and a nice chianti. --

※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 218.161.116.12 ※ 文章網址: https://webptt.com/m.aspx?n=bbs/NTU-Exam/M.1472290880.A.318.html ※ 編輯: zodiac733 (218.161.116.12), 08/27/2016 17:46:27