課程名稱︰熱物理 課程性質︰物理系必修 課程教師︰蔡政達 教授 開課學院：理學院 開課系所︰物理學系 考試日期（年月日）︰2020/12/1 考試時限（分鐘）：110分鐘 試題 : 1. The equation of state of a certain gas is (P+b)v=RT and its specific internal energy is given by u=aT+bv+u_0 (a) Find c_v (10 points) (b) Show that c_P-c_v = R (10 points) 2. Assume that the specific internal energy of an ideal gas is given by u=u_0+(c_v)*(T-T_0), u_0=constant. (a) Show that the Joule coefficient is zero (10 point) (b) Show that the Joule-Thomson coefficient is zero (10 point) 3. A Carnot engine is operated between 2 heat reservoirs at temperatures of 400K and 300K. (a) If the engine receives 1200 kcal from the reservoir at 400K in each cycle, how much heat does it reject to the reservoir at 300K? (5 points) (b)If the engine is operated as a refrigerator and receives 1200 kcal from the resvoir at 300K, how much heat does it deliver to the reservoir at 400 K? (5 points) (c) How much work is done by the engine in each case? (5 points) (d)What is the efficiency of the engine in (a) and the coefficient of performance in (b)? (5 points) 4.(a) Show that for reversivel changes in temperature at constant volume, c_v = T*(∂s/∂T)_v (10 points) (b)Assume that c_v = aT+bT^3 for a metal at low temperatures. Calculate the variation of the specific entropy with temperature. (10 points) 5.In your opinion, what's the most important equaiton in classical thermodynamics ? Explain why. (20 points) --End-- 20 points for each question, 100 points in total. --

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