me328:spring 2007 endterm test ---------------- Name________________________________________
* Closed notes, open book test. You may also use a single handwritten 8.5 x 11" help sheet.
* Answer any four of the six questions. Each question is worth 50 points. Please indicate which questions you do not wish to have graded by drawing a line through the respective question statement.

[Some of the numerical answers to the problems below are shown in red]
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Note: Questions 1 and 2 both relate to similar reheat steam power plants, one with an open feedwater heater and one without, however the questions are entirely independent. If you wish to solve both questions then they should both be plotted on the single pressure-enthalpy [P-h] diagram provided below, however please be sure to identify each station on the diagram with the exact station number as indicated on the system diagrams shown below.
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1. Consider the reheat steam power plant operating under the conditions shown in the following diagram:

• a) Carefully plot the complete reheat cycle above on the pressure-enthalpy [P-h] diagram provided below, indicating clearly all 6 stations on the diagram.
• b) using the conditions shown on the diagram above and values obtained from the steam tables, determine the enthalpy values at all six stations
• c) determine the combined work output of both turbines [1431.7 kJ/kg]
• d) determine the thermal efficiency [h_th] of this power plant. (You may neglect the pump work for this evalution.) [37.1%]
• e) Plot both the actual and the isentropic turbine processes of both turbines on the enthalpy-entropy [h-s] "Mollier" diagram provided below. Indicate the specific work done by both the actual and isentropic turbines on the h-s diagram. Based on this plot decide if both turbines are feasible,

Note: Justify all values used and derive all equations used starting from the basic equation for a flow system, and basic definition of thermal efficiency of a heat engine.
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2. In the diagram below the steam power plant described in Question 1 has been augmented with an open feedwater heater in order to provide a de-aerator capability as well as to improve the cycle efficiency. The mass fraction [y] bled off from station (2) has been chosen such that station (8) is at a saturated liquid state.

• a) Carefully plot the complete cycle above on the pressure-enthalpy [P-h] diagram provided below, indicating clearly all 8 stations on the diagram.
• b) using the conditions shown on the diagram above and values obtained from the steam tables, determine the enthalpy values at all eight stations
• c) determine the mass fraction [y] of steam bled from the outlet of the HP turbine at station (2) in order to produce a saturated liquid at station (8). [y = 0.224]
• d) determine the combined work output of both turbines [1233.3 kJ/kg]
• e) determine the thermal efficiency [h_th] of this power plant. (You may neglect the pump work for this evalution.) [39.6%]

Note: Justify all values used and derive all equations used starting from the basic equation for a flow system, and basic definition of thermal efficiency of a heat engine.
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3. Generally, people feel most comfortable when the air is in the "comfort zone": the temperature is between 22°C and 27°C and the relative humidity is between 40% and 60%. Outside air at 35°C and 60% relative humidity is to be conditioned for an office building by cooling and heating so as to bring the air to within the comfort zone. Using the psychrometric chart provided below, neatly plot the required air conditioning process showing clearly the boundaries of the "comfort zone" and estimate the following:

• a) the amount of cooling [48 kJ/kgdry air] and heating [10 kJ/kg dry air] required [kJ/kg dry air]
• b) the amount of moisture removed during the process [11.5 g water/kg dry air]
• c) the final temperature [~24°C] and relative humidity [~53%] of the conditioned air.

Clearly indicate all the estimated values on the psychrometric chart.

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4. Ethane [C₂H₆] is burned with 180% theoretical air, which enters a combustion chamber at 25°C. Assuming complete combustion and a total pressure of 1 atm (101.32 kPa), determine:

• a) the air-fuel ratio [29 kg air/kg fuel]
• b) the percentage of CO₂ by volume in the products [6.35%]
• c) the dew-point temperature of the products [45°C]

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5. An ideal air-standard Diesel cycle engine has a compression ratio of 18 and a cutoff ratio of 2. At the beginning of the compression process, the working fluid is at 100 kPa, 27°C. Neatly sketch the pressure -volume [P-v] diagram for this cycle, and using the cold air standard assumptions determine:

• a) the temperature and pressure of the air at the end of each process
• b) the net work output per cycle [600 kJ/kg]
• c) the thermal efficiency [h_th] of this engine cycle. [63%]

Note: Justify all values used and derive all equations used starting with the basic energy equation for a non-flow system and the basic definition of boundary work done (if required). You may use the ideal gas equation of internal energy change [Du], enthalpy change [Dh], and the P, v, T relations for an ideal gas isentropic process.
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6. We wish to do an initial evaluation of an air-conditioner proposed for an extremely warm and humid environment, in which an evaporative (swamp) cooler would be ineffective because of the high humidity. A novel suggestion is to use an extremely low-pressure water/steam vapor-compression air conditioning system, as sketched in the figure below. Notice the de-aerator pump and accumulator, in which the saturated liquid water at station (3) (10 kPa) is pumped to a pressure of 100 kPa at station (4) before entering the throttle.

Carefully draw the complete air conditioning cycle above on the P-h diagram provided, showing clearly all five processes (1) - (2) - (3) - (4) - (5) - (1). Using the conditions shown on the diagram above and values obtained from the steam tables, evaluate the Coefficient of Performance (COPAC) of the air conditioning system. In this case we define the COPAC as the heat transferred to the evaporator divided by the work done on the compressor plus the work done on the de-aerator pump. [COPAC = 5.1]

Justify all values used and derive all equations used starting from the basic steady flow energy equation.