Instructions: Show all work for complete credit. Work in symbols first, plugging in numbers and performing calculations last. / 26.

Transcription

1 CM ROSE-HULMAN INSTITUTE OF TECHNOLOGY Name Circle sectin: 01 [4 th Lui] 02 [5 th Lui] 03 [4 th Thm] 04 [5 th Thm] 05 [4 th Mech] ME301 Applicatins f Thermdynamics Exam 1 Sep 29, 2017 Rules: Clsed bk/ntes exam. Help sheet allwed. (8-1/2 x 11" sheet f paper, ne side, handwritten; may nt cntain wrked ut example prblems) Maple, Excel, and MATLAB are allwed n yur laptp, but, nthing may be prepared befre the exam. Either pen prperty tables (hardcpies) r pen Prperty Calculatr Prgrams n yur laptp. Instructins: Shw all wrk fr cmplete credit. Wrk in symbls first, plugging in numbers and perfrming calculatins last. Prblem 1 Prblem 2 Prblem 3 / 26 / 37 / 37 Ttal /100

2 PROBLEM 1 [26 pints] (a) [20 pts] Indicate whether each f the fllwing statements is true r false. True False Anything that generates entrpy als destrys exergy. True False Exergy and energy have the same dimensins. True False If a substance is at the same temperature as the envirnment (i.e., T = T 0) then it necessarily has n exergy. True False Exergy is a cnserved prperty. True False Isentrpic efficiency and exergetic efficiency are necessarily the same thing. True False Based n its definitin, exergy cannt be negative. True False When heat is transferred int a system, it necessarily transfers entrpy int the the system. True False When heat is transferred int a system, it necessarily transfers exergy int the the system. True False Exergy destructin is a cnsequence f the Secnd Law f Thermdynamics. True False A turbine with 101% isentrpic efficiency is thermdynamically impssible.

3 (b) [3 pts] Heat transfer in the amunt f 100 kj is transferred t air in a rigid cntainer. The reservir is at T R = 500 K and the envirnment are at T 0 = 300 K and P 0 = 100 kpa. Hw much exergy has been transferred t the air? 100 kj -100 kj 40 kj -40 kj 20 kj Insufficient infrmatin t determine (c) [3 pts] Pwer in the amunt f 100 kw is transferred t air in a rigid cntainer in a steadystate prcess. The envirnment are at T 0 = 300 K and P 0 = 100 kpa. Hw much exergy has been transferred t the air? 100 kw -100 kw 66.7 kw kw 33.3 kw Insufficient infrmatin t determine

4 PROBLEM 2 [37 pints] A mass f 0.75 kg f saturated liquid steam is initially cntained in a pistn cylinder initially at P 1 = 200 kpa. Heat transfer in the amunt f kj is added t the steam in a cnstant pressure prcess until the quality reaches x 2 = 0.6. The heat is transferred frm a thermal reservir maintained at T R = 227 C while hlding the pressure f the steam cnstant. The envirnment is at P 0 = 100 kpa and T 0 = 300 K. steam TR = 227 C (a) Sketch the prcess n P-v and T-s diagrams. (b) Calculate the wrk ut f the steam in kj. (c) Calculate the useful wrk ut f the steam in kj. (d) Using the Accunting f Exergy Equatin, find the ttal exergy destryed in the prcess.

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6 Prblem 3 [37 pints] A flw f mm aaaaaa= 10 kg/s f air is cmpressed adiabatically in a cmpressr with an isentrpic (adiabatic) efficiency f η C=0.8. The exiting air is then expanded irreversibly thrugh a thrttle valve t a lwer pressure. The valve perates adiabatically and has n mving parts. The apparatus and pertinent prperty values are shwn in the diagram at the right. P2 = 5.0 bar T2 = 220 C WW cc,iiii=? valve (2) (3) P3 = 4.0 bar ηc = 0.8 Treat air as an ideal gas with variable specific heats. The envirnment is at P 0 = 100 kpa and T 0 = 27 C. (a) Sketch the tw-step prcess n a T-s diagram. (b) Calculate the cmpressr input pwer in kw. (c) Calculate the exergetic efficiency f the cmpressr. (d) Using any reasnable methd, find the ttal rate f exergy destructin in the valve. Remember that the valve perates adiabatically and has n mving parts. (1) P0 = P1 = 1.0 bar T0 = T1 = 27 C mm aaaaaa= 10 kg/s

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8 Length 1 ft = 12 in = m = 1/3 yd 1 m = 100 cm = 1000 mm = in = ft 1 mile = 5280 ft = m Mass 1 kg = 1000 g = lbm 1 lbm = 16 z = kg 1 slug = lbm Temperature Values (T/K) = (T/ R) / 1.8 (T/K) = (T/ C) (T/ C) = [ (T/ F) 32 ]/1.8 (T/ R) = 1.8(T/K) (T/ R) = (T/ F) (T/ F) = 1.8(T/ C) + 32 Temperature Differences ( T/ R) = 1.8( T/K) ( T/ R) = ( T/ F) ( T/K) = ( T/ C) Vlume 1 m 3 = 1000 L = 10 6 cm 3 =10 6 ml = ft 3 = gal 1 ft 3 = 1728 in 3 = gal = m 3 1 gal = ft 3 = m 3 1 m 3 /s = ft 3 /s = gal/s 1 ft 3 /s = m 3 /min = gal/s = gal/min Frce 1 N = 1 kg m/s 2 = lbf 1 lbf = 1 slug ft/s 2 = lbm ft/s 2 = N Pressure 1 atm = kpa = bar = lbf/in 2 1 bar = 100 kpa = 10 5 Pa 1 Pa = 1 N/m 2 = 10-3 kpa 1 lbf/in 2 = kpa = N/m 2 ; [ lbf/in 2 = psi ] Energy 1 J = 1 N m 1 kj = 1000 J = ft lbf = Btu 1 Btu = kj = ft lbf 1 ft lbf = J Energy Transfer Rate 1 kw = 1 kj/s = ft lbf/s = hp = Btu/s 1 Btu/s = kw = hp = ft lbf/s 1 hp = 550 ft lbf/s = kw = Btu/s Vlumetric Flw Rate Specific Energy 1 kj/kg = 1000 m 2 /s 2 1 Btu/lbm = ft 2 /s 2 1 ft lbf /lbm = ft 2 /s 2