EXAM # 2. First Name Last Name CIRCLE YOUR LECTURE BELOW: INSTRUCTIONS

Transcription

1 CIRCLE YOUR LECTURE BELOW: First Name Last Name Div. 1 08:30 am Prof. Chen Div. 2 11:30 am Prof. Braun EXAM # 2 INSTRUCTIONS 1. This is a closed book examination. You are allowed to have two single sheets of 8.5 in. x 11 in. paper with notes on both sides for the examination. All needed property tables are provided. 2. Do not hesitate to ask the instructor if you do not understand a problem statement. 3. Start each problem on the same page as the problem statement. Write on only one side of the page. Materials on the back side of the page will not be graded. 4. Put only one problem on a page. A second problem on the same page will not be graded. 5. If you give multiple solutions, you will receive only a partial credit although one of the solutions is correct. Delete the solutions you do not want. 6. For your own benefit, please write clearly and legibly. Maximum credit for each problem is indicated below. 7. After you have completed the exam, at your seat, put your papers in order. This may mean that you have to remove the staple and re-staple. Do not turn in loose pages. 8. Once time is called you will have three minutes to turn in your exam. Points will be subtracted for exams turned in after these three minutes. Problem Possible Score Total 100 1

2 Problem 1. (20 points) This problem consists of 10 parts. Each part is 2 points. Place your brief answers in the boxes. a) Is the statement correct? For the Dalton model, the volume of an ideal-gas mixture is equal to the sum of the volumes of individual gas in the mixture. b) Is the statement correct? For the Dalton model, the pressure of an ideal-gas mixture is equal to the sum of the partial pressures of each individual gas in the mixture. c) Is the statement correct? The specific internal energy of an ideal gas mixture is equal to the sum of the specific internal energy of each individual gas in the mixture? d) For the same inlet air temperature, which inlet humidity condition would provide cooler outlet air temperatures for an evaporative cooler: 1) higher humidity, 2) lower humidity, 3) no difference? e) Steam at 25 o C is added into the air in a room at the same temperature. Will the room air temperature increase, decrease, or remain the same? f) Is it possible to obtain saturated air from unsaturated air without adding any moisture? g) Which equation would be more accurate for O 2 gas at a pressure of 200 bar, the ideal gas equation or Redlich-Kwong equation? h) Does the Clapeyron equation use any approximations? i) Through analysis of a vapor power cycle, it has been determined that the entropy production for the whole cycle is positive but one of the processes in the cycle has a negative entropy production. Is the vapor power cycle possible? j) When the simple ideal Rankine cycle is modified with regeneration, does the heat addition to the cycle increase, decrease, or remain the same for the same boiler pressure, condensing pressure, and maximum temperature? 2

3 Problem 2. (30 points) Ambient air is at 25 o C and 40 percent relative humidity under the local atmospheric pressure of 100 kpa. a) Complete the following table for the ambient air by using the following psychrometric chart: Dry bulb temperature ( o C) Wet bulb temperature ( o C) Dew-point temperature ( o C) Humidity ratio (kg v /kg dry air ) Enthalpy (kj/kg dry air ) Specific volume (m 3 /kg dry air ) b) Determine the vapor pressure of the ambient air, in kpa c) Draw the processes (lines) of an air conditioning system on the psychrometric chart if the ambient air (state 1) is humidified by injection of liquid water at the ambient wet bulb to saturation (state 2) and then cooled to 6 o C (state 3) using a cooling coil. Label the states accordingly on the chart. 3

4 d) Determine the amount of liquid water needed to humidify 2 m 3 /s of the air from state 1 to state 2, in kg/s. e) If the humidifier is eliminated from the system in part c, would it be possible to achieve state 3? Explain how and depict the process(es) on the psychrometric chart. Would this system require more, less, or the same cooling energy as the system of part c? 4

5 Problem 3. (10 points) Derive the following equation for enthalpy difference of a gas whose equation of state is p(v a) = RT and assuming a is a constant and specific heats are constant. h 2 h 1 = C p (T 2 T 1 ) + a (p 2 p 1 ) Note h h v Cp and v T T p p T T p 5

6 Problem 4. (40 points) A steam power plant operates on an ideal cycle as shown in the following figure and provides both power output and heat for a process. Superheated steam with a flow rate of 20 kg/s leaves the boiler at 10.0 MPa and 400 o C. Exactly 2.0 kg/s of steam leaving the boiler is throttled to an intermediate pressure of 4.0 MPa and is routed to the process heater (state 5). Half of the remaining steam entering the turbine is extracted from the turbine at 4.0 MPa for the process heater. The remaining steam in the turbine continues to expand to 20 kpa. States 1 and 8 are saturated liquid water. The pumps and turbine stages are isentropic. The pressure drops and heat losses in the piping are negligible. 20 kg/s 9 a) Show the cycle on the T-s diagram on the next page, including state point labels b) Complete the table below, excluding the shaded cells c) Determine the heat rate extracted from the process heater, in kw d) Calculate the total power output from the turbine (both stages), in kw e) Calculate the power input to pump 1, in kw State P [MPa] T [ o C] v [m 3 /kg] h [kj/kg] s [kj/kg-k] x or region Subcooled Subcooled Superheated Subcooled Assumptions: Steady state, Steady flow, ke = 0, pe = 0, the pumps, turbine, and expansion valve are adiabatic, no heat losses or gains from the pipe lines, liquid water is incompressible 6

7 a) T s Please circle your answers b) 7

8 Please circle your answers 8

9 Please circle your answers 9

10 Please circle your answers 10