Last Nae: First Nae: Thero no. ME 00 Therodynaics 1 Fall 018 Exa 1 Circle your instructor s last nae Division 1 (7:0): Naik Division (1:0): Wassgren Division 6 (11:0): Sojka Division (9:0): Choi Division 4 (8:0): Holloway Division 7 (:0): Vuppuluri Nuber of extra papers used if any Division 8 (1:0): Buckius INSTRUCTIONS Do not reove staples fro any page. If you use extra paper, attach it at the end of the exa with a paper clip and indicate above how any extra sheets were attached. Do not write on the back of any page because it will not be scanned so will not be graded. This is a closed book and closed notes exa. Equation sheets and all needed tables are provided. Significant credit for each proble is given if you identify your syste and its boundary, draw the relevant energy flows on a diagra i.e. Energy Flow Diagra (EFD), start your analysis with the basic equations, list all relevant assuptions, and have appropriate units and use three significant figures. There is no need to re-write the given and find. Do not hesitate to ask if you do not coprehend a proble stateent. For your own benefit, please write clearly and legibly. You ust show your work to receive credit for your answers. IMPORTANT NOTE The use of PDAs, Blackberry-type devices, cell phones, laptop coputers, sart watches or any other sources of counication (wireless or otherwise) is strictly prohibited during exainations. Doing so is cheating. If you bring a sart watch, cell phone, or other counication device to the exaination, it ust be turned off prior to the start of the exa, placed in your backpack, and the backpack ust be stored below your seat. It shall be reactivated only after you leave the exaination roo for the final tie. Otherwise it is a for of cheating and will be treated as such. SECOND IMPORTANT NOTE The only calculators allowed for use on this exa are those of the TI-0X series. No others. 1
Last Nae: First Nae: Thero no. 1. [0 points] Circle the correct answer (no partial credit) for (a) to (c). [ points each] (a) For a substance near saturation doe (on either side of it/under it), phase can always be deterined knowing pressure and teperature. (True or False) e.g. water 1 bar and 99.6C saturated liquid/saturated vapor/saturated ixture (b) For a substance near saturation doe (on either side of it/under it), phase can always be deterined knowing pressure and specific volue. (True or False) e.g. water 1 bar and 1.8 / superheated vapor (c) At critical point, the specific internal energy of saturated liquid is equal to specific internal energy of saturated vapor. (True or False) (d) A constant ass syste, having negligible changes in KE and PE, is supplied with 0 of work and heat transfer of 50 occurs fro the syste to surroundings. Does the energy of the syste (decrease or increase or reain the sae)? Justify using an equation. [7 points] QW E U KEPE U 50 ( 0 ) 0 energy decreases (e) A closed, rigid tank contains a saturated liquid-vapor ixture (v < v critical ). When the tank is heated to a pressure below critical pressure, the possible final phase(s) is/are (saturated liquid-vapor ixture, saturated liquid, saturated vapor, copressed liquid, superheated vapor). Justify using a P-v diagra. [7 points] Depending on the aount of heat transfer, saturated liquid-vapor ixture or saturated liquid or copressed liquid are possible phases
Last Nae: First Nae: Thero no.. [40 points] Water substance with an absolute pressure of 1 bar and a quality of 0.5 (State 1) is expanded in a closed piston-cylinder device along a path for which Pv 1.5 = constant until the absolute pressure drops to 0.5 bar (State ). (a) Find the final quality. Report your answer in %. (b) Calculate the work per unit ass of water during the process. Report your answer in /. (c) Deterine the heat transfer per unit ass of water during the process. Report your answer in /. (d) Show the process on a P-v diagra relative to the vapor doe and the lines of constant teperature for the two states. Label the axes, two states, and indicate the process direction with an arrow. Identify the syste, show ass/energy interactions (EFD), list any assuptions and basic equations, and provide your solution. There is no need to re-write the given and find. Syste/EFD W Assuptions Q Quasi-equilibriu Ignore KE change Ignore PE change Closed = constant Neglect friction No other work except boundary work Syste = Water inside the cylinder State 1 P 1 = 1 bar x 1 = 0.5 State P = 0.5 bar Basic Equations Wboundary de dt syste pdv Integrating: QW U KE PE z xz 1 x z ixture g f in in Q W h ke pe h ke pe in out out out
Last Nae: First Nae: Thero no. Extra Space for Proble Solution (a) State 1: v f 1 bar 0.00104 and vg 1 bar 1.699 v1 xv 1 g 1x1vf 0.51.699 0.750.00104 0.44 1.5 1.5 For the given process path: Pv 1 1 Pv v 0.67 State : v f 0.5 bar 0.001099 and vg 0.5 bar.4 v v v saturated liquid-vapor ixture f g g v x v 1x v Final quality: x f v v g v f v f x 0.08 or 0.8% constant Pv 1 1 Pv (b) Specific work during the expansion process: w1 Pdv dv n v n1 1100kPa0.44 0.5100kPa0.67 w1 w1 17.5 w > 0 work done 1.5 1 by the syste (c) Considering energy balance, specific heat transfer during the expansion process: q1 w1 u u1 State 1: u f 1 bar 417.40 and ug 1 bar 505.6 u1 xu 1 g 1x1uf 0.5505.6 0.75417.4 99.5 State : u f 0.5 bar 40.49 and ug 0.5 bar 48. u xug 1xuf 0.0848. 0.7940.49 786. q 1 17.5 786. 99.5 q 16 q < 0 heat transfer out of the syste 1 4
Last Nae: First Nae: Thero no. Extra Space for Proble (d) P-v diagra 5
Last Nae: First Nae: Thero no.. [40 points] A piston-cylinder device contains air, stops, and a linear spring as shown in the figure below. Air initially occupiess a volue of 0.5 at an absolute teperature of 1000 K (State 1) when the spring is touching the piston without exerting any force. Air is cooled until the pistonn hits the stops when the volue of air is 0. (State ). Further cooling of air decreases the absolute teperature of air to 50 K (State ). The ass of the piston is 0, its cross-sectional area is 0.0, and the spring constant is 1000 N/. Molecular weight of air: 8. 97 /kol (a) Draw a free body diagra for the piston showing appropriate forces at State 1 and calculate absolute pressure of air at State 1. Report your answer in kpa. (b) Deterine the displaceent of the piston corresponding to the volue change fro State 1 to State. Report your answer in. (c) Draw a free body diagra for the piston showing appropriate forces at State and find absolute pressure of air at State. Report your answer in kpa. (d) What is the absolute pressure of air at State? Report your answer in kpa. (e) Show the two processess on P-V diagra. Label the axes and three statess and indicate the two process directions with arrows. (f) Find the boundary work for air in the cylinder fro State 1 to State. Report your answer in. Identify the syste on the sketch provided, show ass/energy interactions (EFD), list any assuptions and basic equations, and provide your solution. There is no need to re-write the given and find. 6
Last Nae: First Nae: Thero no. Extra Space for Proble Assuptions Quasi-equilibriu Neglect friction Air behaves as an ideal gas Closed = constant No other work except boundary work Basic Equations Wboundary pdv pv R T ; R air Solution (a) Considering free body diagra of the piston at State 1: Fair,1 Fat Wpiston PA 1 Pat A g Pressure of air at State 1: P1 107 kpa air R MW 0 9.81 g s P1 Pat 100 kpa kpa A 0.0 1000 air (b) Displaceent of piston fro State 1 to State V1 V 0.5 0. x x 10 A 0.0 (c) Considering free body diagra of the piston at State : F F F W P Ak x P A g air, spring at piston spring at Pressure of air at State : g kspring x P P at 106.5 kpa. kpa A A F at W piston P 7. kpa F air, F spring 7
Last Nae: First Nae: Thero no. Extra Space for Proble (d) For process 1-: PV PV P V 7. kpa 0. air T T 1000 K T 75 K R T R T P V 1 1 1 air 1 air 1 1 106.5 kpa 0.5 For process -: air PV PV P T P RairT RairT P T 75 K 50 K 7. kpa Pressure of air at State : P 66.5 kpa (e) P-V diagra (f) Boundary work during the process fro State 1 to : 1 W pdv Area under the curve (line)fro 1to P P V V 1 1 1 1 1 W1 106.5 7. kpa 0. 0.5 W 1 7 8
Last Nae: First Nae: Thero no. Extra Space for Proble 9