(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, T_H, (2) Isentropic expansion of the medium to a lower temperature, T_L; (3) Heat rejection from the medium at temperature T_L; 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%)

(a) isothermal compression (10%) and

(b) isentropic compression (15%).

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

(b) the exit velocity (10%), and

(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.

(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%)

(a) Derive the so-called Maxwell relations: (10%)

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

(4) The solid M at 1350 K is dissolved in the liquid N at 1350 K, forming the M-N mixing liquid solution. Calculate the total entropy change and the total enthalpy change in the whole process. (10%)

(3) What is the total enthalpy change of M-N mixing liquid solution at 1350 K? (5%)

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