课程名称︰热物理
课程性质︰物理系必修
课程教师︰蔡政达 教授
开课学院：理学院
开课系所︰物理学系
考试日期（年月日）︰2020/12/1
考试时限（分钟）：110分钟
试题 :
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)