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110 年 - 110 國立臺灣大學_碩士班招生考試_應用力學研究所乙組:熱力學(C)#101258 

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(1) Air is compressed steadily by a reversible compressor from an inlet state of temperature Tland pressure Pl to an exit state of pressure P2. Let us assume that the gas behaves as an ideal gas, and xis the specific heat ratio. Determnine the compressor work per unit mole for

【題組】 (a) isothermal compression (10%) and

2.【題組】(b) isentropic compression (15%).

(2) Steam is leaving a 4-liter pressure cooker whose operating pressure is 150 kPa. It is observed that the amount of liquid in the cooker has decreased by 0.6 liter in 40 minutes after the steady operating conditions are established, and the cross-sectional area of the exit openting is 8 mm2. Determine

【題組】 (a) the mass fow rate of the steam (10%),

4.【題組】(b) the exit velocity (10%), and

5.【題組】(c) the flow work per unit mass (5%). At 150 kPa, we know that the specific volume for saturated liquid water and saturated water vapor are vf= 0.001053 m3/kg and vg= 1.1594 m3/kg, respectively. The internal energy for saturated liquid water and saturated water vapor are uf= 466.97 kJikg and ug= 2519.2 kJfkg, respectively. The enthalpy for saturated liquid water and saturated water vapor are hf = 467.13 kJkg and hg = 2693.1 k.I/kg, respectively.


(3) Heat engines are devices for converting thermal energy to work, and their performance are expressed in terms of thermal efficiency, 61414fdb4d1bc.jpgis the heat input per unit mass of the fuid mediut (assumed ideal gas here).6141509b4e47e.jpg614150bd22fd7.jpg

【題組】(a)The most effective (also idealized) engine is operated under a Carnot cycle, which consists four processes: (1) Heat addition to the medium at a temperature, TH, (2) Isentropic expansion of the medium to a lower temperature, TL; (3) Heat rejection from the medium at temperature TL; and (4) Isentropic compression of the medium back to temperature TH. Plot the T-s (termperature-entropy) diagram and p-v (pressure-volume) diagram of the process, and derive the thermal efficiency. Discuss the assumptions made in the model. (15%)

7.【題組】(b) For the four-stroke spark-ignition cngines employed in cars as shown in the figure below, Otto cycle is a more realistic model, with the heat addition and rejection processes at constant temperature in the Carnot cycie replaced by processes at constant volume Cheat addition at yolume TDC and heat rejection at volume BDC). Plot the T-s diagram and p-y diagram of the process for the "simplified (simpler than that shown below)" Otto cycle, and derive the thermal eficiency. Discuss the assumptions made in the Otto cycle, and the differences in efficiencies between the Carnot and Otto cycles. (15%)

(4) The Gibbs relations read du =Tds- pdv and dh = Tds+ vdp, where u is the internal energy, h is the enthalpy, T is the temperature, s is the entropy, p is the pressure, and v is the specific volume. In addition, the Helmholtz function a=u-Ts and Gibbs function g = h-Ts .


(a) Derive the so-called Maxwell relations: 6141511cbff33.jpg(10%)


(b) Show that 6141514f4b236.jpgfor an isentropic process of an ideal gas reiating state 1 and state 2, where x is the specific heat ratio. (10%)



24.下圖是小南歷史報告的段落主題,此份報告的標題最可能為下列何者? (A)《殖民與鴉片》 (B)《纏足的理由》 (C)《論薙髮留辮》 (D)《槍枝禁止史》...

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110 年 - 110 國立臺灣大學_碩士班招生考試_應用力學研究所乙組:熱力學(C)#101258-阿摩線上測驗

110 年 - 110 國立臺灣大學_碩士班招生考試_應用力學研究所乙組:熱力學(C)#101258