课程名称︰材料热力学一 课程性质︰必修 课程教师︰林招松 开课学院：工学院 开课系所︰材料系 考试日期（年月日）︰101.10.17 考试时限（分钟）：180 分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : Gas constant R = 8.3144 J/(mole K) = 1.987 cal/(mole K) = 0.082057 (liter-atm)/(mole K) 1. One mole of the ideal gas at P1 atm and T1 K is adiabatically expanded to P2 atm and T2 K. (15%) (1) Prove the work (W) performed during this process is cvY1[1-(P2/P1)^((γ-1)/γ)] if the expansion is performed reversibly. Where cv is the constant volume heat capacity and γ=cp/cv (2) Prove mathematically or schematically the W performed is the maximum work. 2. One mole of a monoatomic ideal gas (cv=3R/2) is subjected to the following sequence of steps a. Starting at 250 K and 5 atm, the gas expands freely into a vacuum to triple its volume. b. The gas is next heated reversibly to 400 K at constant volume. c. The gas is reversibly expanded at constant temperature until its volume is again tripled. d. The gas is finally reversibly cooled to 250 K at constant pressure. Calculate the values of q and w and the change in U, H, and S during each step and the whole sequence. (20%) 3. Draw on the temperature-entropy coordinated the Carnot cycle and based on this diagram, prove the efficiency of the Carnot cycle is equal to 1-(T1/T2), where T1 and T2 are the temperature of the reservoirs at high and low temperature, respectively. Hint: plot the Carnot cycle on the coordinate with temperature as the abscissa and entropy as the ordinate. (15%) 4. (1) Prove that cp-cv = (δV/δT)(←定P)*[P+(δU/δV)(←定T)] (7%) (2) What the (δU/δV)(←定T)*(δV/δT)(←定P) term stands for ? Why (δU/δV)(←定T)*(δV/δT)(←定P) is significant for solids but can be neglected for ideal gases ? (8%) 5. Answer the following question (35%) (1) Is the infinitesimal quantity dF = (x^2-y)dx + xdy an exact differential ? (2) Is thermodynamics first law sufficient to deal with the equilibrium of a single component system ? Why ? (3) For the evaporation of one mole of water in a thermo-stalled piston and cylinder containing water and water vapor, would you expect the amount of heat exchanged with the heat bath during reversible evaporation to be greater than, the same as, or less than the amount of heat exchanged with the heat bath during irreversible evaporation ? Why ? (4) Do you agree the statement: The sum of the entropy change of the system and of the surrounding is always zero. Why ? (5) Name and describe briefly three irreversible processes during which the entropy of the system increases. (6) What is the sponsaneity of an irreversible process ? (7) Show that for an ideal gas δq is not an exact differential but δq/T is. --

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