ENGR -503 Name: Final Exam, Sem. 03C ID N.: /6/003 3:30 5:30 p.m. Rm N.: 7B Fill in yur name and ID N. in the space abve. There shuld be pages (including this page and the last page which is a frmula page). RELAX, this is nly an exam. Read ver the whle exam, then decide which prblem t wrk first. The exam is clsed bk, and tw duble-sided sheets f ntes are permitted in additin t the frmula page attached t this exam. N cllabratin with thers! Fr multiple chice questins, chse the single, BEST answer. Prperties and cnversin factrs are in the bklet prvided. Include a sketch and clearly state assumptins and equatins used n prblems requiring detailed analysis. If yu use data frm a table, indicate the TABLE NUMBER and the value read. Failure t d s will result in a lwer scre. If yu get stuck n a prblem, g t anther ne. Pace yurself by the time and number f pints. Yu shuld spend n average 3.6 minutes per multiple chice prblem and 4 minutes per wrk-ut prblem. Prblems must be wrked in the unit system in which they are specified. Failure t d s will result in a lwer scre. Yu have tw hurs t cmplete the exam. Prblem Pints earned Ttal pints pssible Multiple chice: 60 Wrkut prblem : 0 Wrkut prblem : 0 Ttal: 00
ENGR -503 Final exam, Fall 003 ID N.:. Answers t the multiple chice questins. Circle the letter that crrespnds t yur answer fr each f the multiple chice questins. Please nte that nly the answers yu prvide n this sheet will be graded.. A B C D E. A B C D E 3. A B C D E 4. A B C D E 5. A B C D E 6. A B C D E 7. A B C D E 8. A B C D E 9. A B C D E 0. A B C D E. A B C D E. A B C D E 3. A B C D E 4. A B C D E 5. A B C D E 6. A B C D E 7. A B C D E 8. A B C D E 9. A B C D E 0. A B C D E
ENGR -503 Final exam, Fall 003 ID N.:. I. (60 pts ttal) Multiple chice prblems wrth pints each. Circle the answer that is the mst apprpriate r clsest numerically t yur answer and then select that answer n the answer sheet.. An ideal gas in a rigid cntainer is initially at an abslute pressure f 400 kpa and a temperature f 38 K. If the gas is heated t a final temperature f 73 K, the final abslute pressure in MPa is: a. 0.5 b. 0.9 c..0 d. 4.0 e. Nne f the abve. A gas is cntained in a vertical cylinder with a frictinless, heavy pistn weighing 3 lb f and having a crss-sectinal area f 6 in. The lcal atmspheric pressure is 4.7 psia. What is the abslute pressure inside the cylinder in psia? a..6 b. 4.7 c. 6.8 d..6 e. 83. 3. Water at 400 kpa and 4 C is a a. Subcled liquid b. Saturated liquid c. Saturated liquid-vapr mixture d. Saturated vapr e. Superheated vapr 4. Fr any arbitrary prcess, an ideal gas in a rigid cntainer always maintains a. Cnstant pressure b. Cnstant enthalpy c. Cnstant internal energy d. Cnstant specific vlume e. Cnstant entrpy 3
ENGR -503 Final exam, Fall 003 ID N.:. 5. The quality f a vapr-liquid mixture f R-34A at 0. MPa and having a specific enthalpy f 50 kj/kg is a. 0.00 b. 0.55 c. 0.65 d. 0.75 e..00 6. The air cnditining system ges ut in a well-insulated auditrium that cntains 700 peple and 800 kg f air at 8 C. The windws and drs are clsed s that there is n significant exfiltratin r infiltratin f air. If the heat input frm each persn is 60 W, hw lng in minutes des it take fr the air in the auditrium t reach 30 C. a. b. 6 c. d. 0 e. 00 7. Cnsider a cntrl vlume in which ccurs a steady flw prcess: a. Intensive prperties may change with time b. Extensive prperties may change with time c. All prperties may change with time d. Prperties d nt change with lcatin in the cntrl vlume e. Prperties d nt change with time 8. Fr an adiabatic cmpressr a. The enthalpy is unchanged between the inlet and utlet b. The ptential energy change between the inlet and utlet is large c. The specific wrk input is equal t the enthalpy change d. The specific wrk utput is equal t the enthalpy change e. The wrk input is equal t the heat exchange with the surrundings 4
ENGR -503 Final exam, Fall 003 ID N.:. 9. Steam enters an adiabatic nzzle at 500 kpa, 400 C and 0 m/s and exits at 80 m/s. The specific enthalpy change (h h ) between the inlet and the utlet f the nzzle in kj/kg is a. -3000 b. -6 c. -3 d. 3 e. 3000 0. The air cnditiner unit in a student s apartment has a COP R f 3.. If heat is rejected t the utdr high temperature reservir at a rate f 750 kw, what is the rate f heat remval frm the apartment in kw? a. 80 b. 90 c. 570 d. 400 e. Indeterminate frm the given infrmatin. The entrpy change between states and f an internally reversible prcess is a. Always psitive b. Always negative c. Always zer d. Dependent n the prcess path e. Independent f the prcess path. An isentrpic prcess is ne that is always a. Internally reversible b. Adiabatic c. At cnstant entrpy d. Internally reversible and adiabatic e. Impssible in reality 5
ENGR -503 Final exam, Fall 003 ID N.:. 3. The purpse f the reheat cycle in the Rankine cycle reheat is t a. Make use f high temperature exhaust steam b. Take advantage f higher biler temperatures while maintaining high quality steam exiting the turbine c. Prvide pwer generatin t the circulatin pump d. Lwer the quality f the steam exiting the turbines e. Give thermdynamics students mre enthalpies t calculate 4. Steady, incmpressible, frictinless flw in a hrizntal, unifrm-diameter pipe exhibits a. Cnstant pressure b. Steadily increasing pressure c. Steadily decreasing pressure d. Steadily increasing velcity e. Steadily decreasing velcity 5. An ideal Ott cycle has a cmpressin rati f 8. At the beginning f the cmpressin prcess, the air is at 00 kpa and 90 K; at the end f the cmpressin prcess, the air is at 667 K. 800 kj/kg f heat are transferred t the air during the cnstant-vlume heat-additin prcess. Using the cld air assumptins, the maximum temperature in the cycle in K is: a. 90 b. 75 c. 460 d. 780 e. 990 6. Fr an ideal Braytn cycle with a cmpressin rati f 8, air enters the cmpressr at a temperature f 300 K. Using variable specific heats, the temperature f air exiting the cmpressr in K is a. 80 b. 375 c. 480 d. 540 e. 760 6
ENGR -503 Final exam, Fall 003 ID N.:. 7. Steam enters the isentrpic turbine f an ideal Rankine cycle pwer plant at 3 MPa and 350 C and exits at 75 kpa. The quality f steam exiting the turbine is a. 0.7 b. 0.8 c. 0.9 d..0 (saturated vapr) e. Undefined (superheated steam) 8. Refrigerant-34A enters a cndenser as superheated steam at 0 F and 5 psia and exits as a saturated liquid. The heat rejected t the envirnment frm the cndenser during this prcess in Btu/lb m is a. 6.68 b. 4. c. 8.3 d. 90.0 e. 98.9 9. A water twer is 35 m high and is drained by a 5 cm diameter pipe that runs dwn a hill a length f 000 m and having an elevatin decrease f 5 m (see figure belw). The pressure in the water twer is 00 kpa gauge pressure and the pipe at the bttm f the hill exits t the atmsphere. Neglecting frictinal lsses, the velcity in m/s exiting the pipe at the bttm f the hill is a. 0.6 b. 6 c. 34 d. 49 e. 85 Figure : Sketch fr multiple-chice questin 9. 7
ENGR -503 Final exam, Fall 003 ID N.:. 0. The velcity prfile in a pipe is given by r ur () umax R where r is the radial distance frm the pipe centerline, u max is the maximum velcity in the pipe and R is the radius f the pipe. Given that the shear stress in radial crdinates is given by du τ () r µ dr where µ is the dynamic viscsity, the shear stress at the pipe wall (r R) is given by a. µ umaxr R b. µ umaxr R c. µ u max R d. µ u max R e. nne f the abve 8
ENGR -503 Final exam, Fall 003 ID N.:. II. (40 pts ttal) Wrk-ut prblems wrth 0 pints each. Prblem parts are valued as nted. State all imprtant assumptins and indicate which tables yu are reading values frm.. Steam enters a real turbine at 0 MPa and 500 C at a rate f kg/s and leaves at 0 kpa. The net pwer utput frm the turbine is.6 MW. Heat is als lst frm the turbine at a rate f 0.4 MW due t imperfect insulatin and irreversibilities in the turbine. Neglecting kinetic and ptential energy changes, determine the fllwing (5 pints each): a. The temperature f the steam exiting the turbine in C. b. The quality f the steam exiting the turbine. c. The specific entrpy change in the turbine in kj/(kg K). d. What wuld be the effect n the net wrk utput f increasing the pressure at the utlet f the turbine? Please explain yur answer. 9 (Cntinue n back f page)
ENGR -503 Final exam, Fall 003 ID N.:.. A gas turbine pwer plant perates n the simple Braytn cycle with air as the wrking fluid and has a pressure rati f 0. The air enters the cmpressr at 90 K and the turbine at 5 K. Bth the cmpressr and the turbine have an isentrpic efficiency f 0.85. Using the cld air apprximatin, determine: a. The air temperature at the cmpressr exit (7 pints) b. The back wrk rati (percent f the ttal wrk utput frm the turbine that ges int the cmpressr). (7 pints) c. The cycle thermal efficiency (6 pints). 0 (Cntinue n back f page)
ENGR -503 Final exam, Fall 003 ID N.:. Pρgh Pv RT PV mrt P v ϕp sat@t T R T/ T cr P R P/ P cr Pv Z RT R R u /M W V I I R w Pdv W m Pdv dh c p dt inlets elect m m i utlets ( f Q ha T b T h u + Pv c p c v + R Q W + inlets ) dm dt cv m ( h + V i i i / v x v f + x(v g -v f ) u x u f + x(u g - u f ) h x h f + x(h g - h f ) dt Q -κa dx m du c v dt Q εσa(t 4 s T 4 surr vapr x KE m( V V ) mliquid + mvapr + gz ) i utlets m ( h + V / + gz ) de/dt ) PE mg(z z) q-w u+ ke+ pe d Q W (U + KE + PE) Q-W U+ KE+ PE dt δq T 0 Clausius Inequality ds δq/t---> reversible Tds du + Pdv Tds dh νdp s s s R p pv pv ln W fr n W p n V pvln V fr n s Cp ln(t / T ) R ln(p / P ) P Pr V Vr ideal gas,cnst prp isentrpic, variable s Cv ln(t / T ) + R ln(v / v) P Pr V Vr prperties, ideal gas sc p ln(t /T ) incmpressible k p v isentrpic, ideal gas W Q H - Q L (Q H /Q L ) rev T H /T L p S Q T heat reservir ( k ) k k T P V / isentrpic ideal gas T P, V COP Q H /W in (heat pump) η W net /Q H (heat engine, pwer cycle) COP Q L /W in (refrig. systems) v p V + ρ g g + z p V + + z ρ g g p p 4l z z g g ρ ρ Dρ g + + τ H L ne dimensinal flw: m ρ VA Re VD ρ ν µ/ρ µ IDEAL GAS CONSTANT: R u 8.34 kpa m 3 /(kml K) R u 8.34 kj/(kml K) R u.986 Btu/(lbml R) R u 545 ft lb f /(lbml R) Q S ds Q cv j + S gen min sin mut sut S gen T dt + + j T inlets utlets Ws η c W a ; η t b Wa ; ηn W s ( ke) ( ke) a s ; η d j ( ke) s ( ke) a H L f l D V g Q S T rev frreservir