(1b). (2.5p) Please mark the region representing the superheated vapor: (A) Region A. (B) Region B. (C) Region C. (D) Region D. (E) None of above.

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1 MAE 20 Thermdynamics Fall 2016 Hmewrk # SOLUTION This hmewrk is de Friday, September 2 rd, 2016 Each prblem is wrth the pints indicated in the parentheses While a cllective wrk n the assignments is allwed and encraged, a brte cpying f the sltin frm yr fellw-stdents is absltely nt acceptable; see Dean ilent s Mem (1) (20 pints) Mltiple chice qestins Σ (1a) (25p) Please circle the item(s), which can be cnsidered as pre sbstance(s) in Thermdynamics: (A) Drinking water (H 2 O) with ice (B) A mixtre f liqid and gases nitrgen () Gasline and air in a fel tank (D) A mixtre f drinking water and ethanl (E) A flwing mixtre f N 2 and O 2 at a rm temperatre and atmspheric pressre (1b) (25p) Please mark the regin representing the sperheated vapr: (A) Regin A (B) Regin B () Regin (D) Regin D (E) Nne f abve (1c) (25p) Please circle the prcess (r prcesses) which can ccr in a satrated liqid-vapr mixtre (A) Melting (B) Vaprizatin () ndensatin (D) Sblimatin (E) All f the abve (1d) (25p) Please circle the valid statement(s) abt cmpressed liqid at temperatre T and pressre P: (A) T < (the satratin temperatre at given pressre P) T P P T T v T (B) P < (the satratin pressre at given temperatre T) () (specific internal energy) (D) v > (specific vlme) (E) x 0 5 (1e) (25p) Please circle a valid statement(s) abt sperheated vapr with temperatre T and pressre P: (A) P > P T T P (B) T > () v > (specific vlme) v T 1

2 (D) (E) < (specific internal energy) T h T h > (specific enthalpy) (1f) (25p) Please circle the item representing the changes in specific enthalpy dring evapratin prcess nder cnstant pressre: f, g, fg, h fg, v fg (1g) (25p) The satrated liqid line and the satrated vapr line intersect in a (A) Triple pint (B) ritical pint () Sperheated pint (D) It depends in whether a P-v diagram r a T-v diagram is cnsidered (E) These tw lines never intersect (1h) (25p) Which ne is invalid amng the fllwing statements regarding ideal gas? (A) The cmpressibility factr f ideal gas is eqal t 1 (B) A sbstance can be cnsidered as ideal gas if its cmpressibility factr is in the range 0 < Z < 1 () A sbstance can be cnsidered as ideal gas if its cmpressibility factr is arnd 1 (>095) (D) Ideal gas is a vapr that is arnd (clse t) satrated vapr line (E) Ideal gas is a specific vapr that is far frm satrated vapr line 2

3 (2) (15 pints) Simple alclatin Qestins n Prperty Tables (emply interplatin if necessary) (2a) (2p) Please find the satrated temperatre f H 2 O at 650 kpa Sltin: Table A-5: T kPa (2b) (2p) Please find the satrated pressre f R-14a at 44 Sltin: Table A-11: P 1107 kpa 44 (2c) (p) Please find the satrated temperatre f H 2 O at 812 kpa Sltin: Table A-5: T 17041, T Emply interplatin: T T T T 800kPa 812 kpa 800 kpa 850 kpa 800 kpa 850kPa 024 ( T T ) Tsat 812kPa kpa ( ) (2d) (p) Please find the satrated pressre f R-14a at 52 Sltin: Table A-11: P kpa, P kPa Emply interplatin: sat sat P P P P sat @ P P ( 15291kPa 1862 ) kpa kpa + 0 kpa (2e) (5p) please find the specific internal energy f the sperheated H 2 O vapr at 98 bar and 54 Sltin: We emply dal interplatin f Table A-6, fist in temperatre, and then in pressre: 9MPa,54 9MPa, MPa,400 9MPa, ( ) 9MPa,54 9MPa,50 9MPa,400 9MPa, ( ) bar, Similarly: 10MPa,54 10MPa,400 10MPa 10MPa,50, ( ) 10MPa,54 10MPa,50 10MPa,400 10MPa, ( ) bar,

4 Finally: 98bar,54 100bar,54 90bar 90bar,54,54 98bar 90 bar bar 90 bar + 08 ( ) 98bar,54 90bar,54 100bar,54 90bar,54 ( 2710 )

5 () (15 pints) Please determine the phases f the fllwing sbstances nder given cnditins, and lcate these states/pints in P-T, T-v r P-v diagrams fr each f the fllwing cases Sltin: Key strategy is the fllwing: we first check if sch a system can be a satrated mixtre, and then make r final cnclsin based n this verificatin Y shld check if the pressre and temperatre given in qestin are available in prperty tables (a) (p) H 2 O at 20 MPa and 220 Frm Table A-4 fr H 2 O: P 2196 MPa > 2 0MPa > sperheated H 2 O vapr 220 Alternatively, frm Table A-5: 2MPa < T > sperheated H 2 O vapr (b) (p) R-14a at 52 and 12 MPa Frm Table A-11 fr R-14a: P 1862 MPa > 1 2MPa > sperheated R-14a vapr Alternatively, frm Table A-12: 12MPa < T > sperheated R-14a vapr (c) (p) H 2 O f specific internal energy 25 MJ / at 05 MPa We check first if this is a satrated mixtre Namely, cnsider a satrated H 2 O mixtre at 05 MPa Frm Table A-5: MPa, MPa We MPa > < < > satrated mixtre indeed f g 5

6 (d) (p) R-14a f specific vlme 045 m / at 04 MPa We check first if this is a satrated mixtre Namely, cnsider a satrated R14-a mixtre at 04 MPa 4 m Frm Table A-12: v 10 m m 79, v 04MPa We have v 0 45 > 04MPa v > > sperheated R-14a vapr v g (e) (2p) H 2 O f specific enthalpy 7 MJ / at 04 MPa We check first if this is a satrated mixtre Namely, cnsider a satrated H 2 O mixtre at 04 MPa Frm Table A-5: h MPa, MPa We have h@ MPa > h > > sperheated H 2 O vapr h g 6

7 (4) (16 pints) A pistn cylinder system cntains 15 f cmpressed liqid H 2 O at a pressre f 500 kpa and a temperatre f 100 (state A) Under cnstant pressre f 500kPa, H 2 O is heated t satrated liqid (state B), satrated mixtre f liqid and vapr f a qality f 0 (state ), satrated mixtre f liqid and vapr with a qality f 08 (state D), satrated vapr (state E) and sperheated vapr with a temperatre f 500 (state F) (4a) (4p) Present this prcess in the schematic T-v and P-v diagrams, with each state clearly marked (4b) (6p) Please find the ttal vlme f the system at states B, D and F Sltin: Table A-5: v 500kPa m /, v 500kPa 0748 m / > State B: satrated liqid The specific vlme is given by: v v 500kPa m / Then the ttal vlme is V mv 15 * m / m State D: satrated mixtre f qality x 08 at 500 kpa Then the specific vlme is given by: v ( ) ( ) m m m 1 x v f + xv g Then the ttal vlme is V mv 15 * 0 m / 45 m State F: sperheated vapr > Table A-6: the specific vlme v 500kPa, m / Then the ttal vlme is V mv 15 * m / 1066 m (4c) (6p) Please find the ttal internal energy f the system at states, E and F Sltin: Table A-5: 500kPa 6954 /, 500kPa /, 500kPa / > State : satrated mixtre f qality x 0 at 500 kpa Then the specific internal energy is 1 x + x + x ( ) f g f fg Then the ttal internal energy is U m 15 * / 1829 MJ State E: satrated vapr The specific internal energy is given by / Then the ttal internal energy is U m 15 * / m State F: sperheated vapr: Table A-6: the specific internal 500kPa, / Then the ttal internal energy is U m 15 * 129 / 4695 MJ 7

8 (5) (12 pints) A free-pistn cylinder system cntains 8 f H 2 O that ccpies a vlme f 400 liters at 2 bars The system is sbseqently preheated, isbarically, ntil its temperatre reaches the vale 200 Please determine the phases and ttal internal energy U f H 2 O in the system at the initial and final states Please als present this prcess, schematically, in bth P-v and T-v diagrams Sltin: State 1: The specific vlme at the initial state is v V / m m 005m / Nw let s determine the phase (r phases) at State 1 Let s check if this can be a satrated vapr r liqid r their mixtre Accrding t Table A-5, v 200kPa 0001m /, 200kPa 08858m / Hence, v f < v 1 < v g at State 1 > we deal with a satrated mixtre indeed Its qality is given by v1 v f x 0055 vg v f Then the specific internal energy at the initial state is (Table A-5): 1 x + x + x , ( ) f g f fg 1 and the assciated ttal internal energy at this state is U Als, nte: T1 T kPa m State 2: The system next nderges isbaric preheating (and expansin), sch that P2 P1 200kPa, T2 200 > T 200kPa > we deal with a sperheated vapr at the final state Then the specific internal energy at the final state is (Table A-6), with the ttal internal energy being U m ,

9 (6) (10 pints) Please find the cmpressibility factr f a sperheated H 2 O vapr at 150 bar and 500 sing the fllwing tw methds: (a) the definitin f cmpressibility: Z pv / RT ; and (b) the Nelsn- Obert chart in Figre A-15 Please jstify if H 2 O nder given cnditins can be cnsidered as ideal gas based n the cmpressibility factr calclated The critical pressre, critical temperatre, and gas cnstant R f water can be fnd in Table A-1 Sltin: (a) Fr a sperheated water vapr, Table A-6 yields the specific vlme the nly nknwn parameter in the eqatin: Z pv / RT 1MPa Table A-6: P 150 bar 15MPa, T 500 : v m / 10bar 100kPa m 150bar pv 1bar Table A-1: R > Z K RT ( ) K K (b) Nte: Y need find the redced pressre and redced temperatre f the sperheated water vapr at given temperatre and pressre Table A-1: P cr 22 06MPa 220 6bar ; T cr 647 1K P 150bar Redced pressre: PR 0 68 Redced temperatre: Pcr 2206bar T ( ) K TR 119 T 6471K cr Y can read the cmpressibility factr in the Nelsn-Obert chart: Z 086 ~ 0 87 Nte: The cmpressibility factr btained in (a) by eqatin and (b) sing Nelsn-Obert chart, is cmparable r almst eqivalent Z ideal, gas < 095 > the sperheated water vapr at 150 bar and 500 is nt ideal gas 9

10 (7) (12 pints) Please find the specific vlme f a pre O 2 at 200 K and 20 MPa by the tw methds: (7a) (4p) Emply the ideal gas eqatin Sltin: p 20 MPa 20 x 10 6 Pa T 200 K Mleclar weight M O2 002 /ml (Table A-1) > pv RT TR /M O2 > v R T/( pm O2 ) 26 x 10 - m / (7b) (8p) Use the cmpressibility chart if the critical pint fr O 2 is knwn: T cr 1546K, p cr 505 MPa Sltin: Redced pressre & temperatre: p R p/p c 20/ , T R T/T c 200/ > Table A-15: Z(p R, T R ) Z(04,1) 094 > v actal ZR T/(M O2 p) (094)(0026) 0024 m / The spplementary prblems frm 8th Editin t be 2, 26, 1, 4, 76, 91 in hapter Althgh these prblems will nt be cllected, they are highly recmmended fr yr practice 10