CHAPTER 3 PROPERTIES OF A PURE SUBSTANCE BLANK

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1 CHAER 3 ROERIE OF A URE UBANCE BANK

2 ONNAG/BORGNAKKE UDY ROBEM he poriztion line nd the criticl point Wht is the phse t room pressure, 101 k nd temperture, 20 o C, for the following sustnces: Oxygen, cron dioxide, wter nd R-134. o nswer the question we need to know something out the loction of the phse oundries. For the criticl point we he informtion from le 3.1 or A.2. Room = 293 K = 101 k Oxygen c = 155 K c = 5040 k Cron dioxide c = 304 K c = 7380 k Wter c = 647 K c = k R-134 c = 374 K c = 4064 k From this informtion lone we cn notice: Oxygen hs >> c nd << c so superheted por, recll Fig. 3.5 Cron dioxide hs c nd << c so superheted por, recll Fig. 3.5, nd the ctul phse digrm in Fig.3.6 could e used. Wter hs lower nd much lower thn the criticl point so we need to know how much lower the sturtion pressure is for the lower s shown in Fig.3.7. From the poriztion line we estimte st = 3 k, the higher mens compressed liquid stte. More ccurtely we could look in le B.1.1 nd find st = 2.3 k. R-134 hs lower nd thn the criticl point so we must look up in le B.5.1. For 20 o C we he sturtion pressure of out 573 k the lower room pressure mens we he n expnded por (superheted por) he sttes re shown reltie to the poriztion line in the - digrm elow. he fusion line for wter slnts left for the others it slnts right. wter Cr.. R-134 oxygen CO2

3 ONNAG/BORGNAKKE UDY ROBEM he poriztion line for wter Determine the phse for ech of the following wter sttes using the section B tles nd indicte the reltie position in the -, - nd - digrms. ) 120 o C, 500 k ) 120 o C, 0.5 m 3 /kg ) Enter le B.1.1 with 120 o C sturtion pressure is k so we he compressed liquid. ht is oe the sturtion line for 120 o C. We could lso he entered le B.1.2 with 500 k nd found the sturtion temperture s o C so we would sy it is sucooled liquid. ht is to the left of the sturtion line for 500 k s seen in the - digrm. ) Enter le B.1.1 with 120 o C nd notice f = < < g = m 3 /kg so the stte is two-phse mixture of liquid nd por. he stte is to the left of the sturted por stte nd to the right of the sturted liquid stte oth seen in the - digrm. Cr C.. =120 C.. =500 k 152 =198 k 120

4 ONNAG/BORGNAKKE UDY ROBEM he mmoni nd the R-22 tles Determine the phse for ech of the following sttes using the section B tles nd indicte the reltie position in the -, - nd - digrms. ) Ammoni 30 o C, 1000 k ) R k, 0.15 m 3 /kg ) Enter le B.2.1 with 30 o C, sturtion pressure is 1167 k s we he lower it is superheted por stte. We could lso he entered with 1000 k nd found sturtion temperture slightly less thn 25 o C so we he stte tht is superheted out 5 o C Cr.. C C C C k ) Enter le B.4.1 with 200 k nd notice > g m 3 /kg so from the - digrm the stte is superheted por. We cn find the stte in le B.4.2 etween 40 o C nd 50 o C. 200 Cr C C 40-25C -25 C k

5 ONNAG/BORGNAKKE UDY ROBEM Wter tles Determine the missing property of -- nd x if pplicle for the following sttes for wter. ) 140 o C, 5000 k ) 200 k, 0.25 m 3 /kg ) Enter le B.1.1 with 140 o C nd we see sturtion pressure of k so t 5000 k we he compressed liquid. We could lso he strted in le B.1.2 with 5000 k nd seen the o C sturtion temperture so since the stte is t lower we he compressed liquid (sucooled). roceed to le B.1.4 susection for 5000 k with the numer fter the 5000 k s the sturtion temperture (oiling for tht ), which here is o C. We get = m 3 /kg. ) Enter le B.1.2 with 200 k nd notice f = < < g = m 3 /kg we he two-phse mixture of liquid nd por t sturtion = o C. he qulity is from Eq.3.10 x = ( f )/ fg = ( ) / = Cr C C 120 C k

6 ONNAG/BORGNAKKE UDY ROBEM he R-22 nd R-134 tles Determine the missing property of -- nd x if pplicle for the following sttes. ) R-22: 30 o C, 1000 k ) R-134: 201 k, 0.1 m 3 /kg ) For R-22 we look in tle B.4.1 with = 30 o C nd notice < st = k so we he superheted por. roceed to tle B.4.2 susection 1000 k ( st = o C). here we find the entry for s: = m 3 /kg Cr C.. C ) For R-134 we look in tle B.5.1 with = 201 k nd notice tht this is ery close to the sturted por stte listed t k. ee lso in B.5.2 susection 200 k where the first entry is the sturted por t 200 k. Interpolte etween these two entries to get g t 201 k g = ( ) = m3 /kg We conclude the stte is superheted (ut ery little) por t roughly 10 o C Cr C.. C k -10

7 ONNAG/BORGNAKKE UDY ROBEM he nitrogen tle Determine the missing property of -- nd x if pplicle for the following sttes. ) Nitrogen: o C, 600 k ) Nitrogen: 100 K, m 3 /kg For nitrogen the properties re listed in le B.6 with temperture in Kelin. ) Enter in tle B.6.1 with = = 220 K, which is higher thn the criticl in the lst entry. hen proceed to the superheted por tles. We would lso he relized this y looking t the criticl properties in tle A.2. From tle B.6.2 in the susection for 600 k ( st = K) = m 3 /kg Remrk: For comprison we find ssuming idel gs, from Eq.3.5 nd tle A.5 s = R/ = kj/kg K 220 K / 600 k = m 3 /kg which differs from the correct lue y less thn one percent. ) Enter in tle B.6.1 with = 100 K nd we see f = < < g = m 3 /kg so we he two-phse stte with pressure s the sturtion pressure st = k nd the qulity from Eq.3.10 ecomes x = ( f )/ fg = ( ) / = Cr C C..

8 ONNAG/BORGNAKKE UDY ROBEM Interpoltion in the superheted wter por tle Determine the pressure for wter t 200 o C with = 0.4 m 3 /kg. trt in le B.1.1 with 200 o C nd notice > g = m 3 /kg so we he superheted por. roceed to le B.1.3 t ny susection with 200 o C, sy we strt t 200 k. here the = which is too lrge so the pressure must e higher. For 500 k ( = ) nd for 600 k ( = ) so it is rcketed C.. C C 200 k A liner interpoltion etween the two pressures is done to get t the desired = ( ) = k he rel constnt cure is slightly cured nd not liner ut for mnul interpoltion we ssume liner rition Notice if we ssume idel gs then = R, R = kj/kg K from le A.5 = R/ = ( ) 0.4 kj K kg kg K m3 = k which is 2% too high, ut resonle pproximtion, see Fig. 3.9, the error goes up for smller s.

9 ONNAG/BORGNAKKE UDY ROBEM A hot-ir lloon nd idel gs lw A hot-ir lloon is inflted with hot ir, 75 o C, t pproximtely 101 k to olume of 775 m 3. How much ir mss is tht? nd how much ir mss t 20 o C, 101 k is displced y the lloon olume? We ssume the ir is n idel gs so we he from Eq.3.5 = mr ; R = kj/kg K from tle A.5 now m = R = ( ) he mss of cold ir displced y the sme olume is m = R = ( ) k m 3 kg K = kj K kg k m 3 kg K = kj K kg o tht size lloon with the hot ir t 75 o C cn lift the difference ( ) kg in the grittionl field, n effect clled the oyncy.

10 ONNAG/BORGNAKKE UDY ROBEM A gs-ell nd mss flow rte A gs-ell is sumerged in liquid wter with its mss counterlnced with rope nd pulleys s shown. he pressure inside is mesured crefully to e 105 k nd the temperture is 21 o C. A olume increse is mesured to e 0.75 m 3 oer period of 185 seconds. Wht is the olume flow rte nd the mss flow rte of the flow into the ell ssuming it is cron dioxide gs? CO2 m he olume flow rte is. = d dt = t = = m3 /s m CO 2 nd the mss flow rte is ṁ = ρ. =. /. At close to room conditions the cron dioxide is n idel gs so = mr or = R/ nd from le A.5 we he the idel gs constnt R = kj/kg K. he mss flow rte ecomes ṁ =. R = ( ) k m 3 /s = kj/kg kg/s

11 ONNAG/BORGNAKKE UDY ROBEM he generlized chrt ropne in steel ottle of olume 0.1 m 3 hs qulity of 10% t temperture of 15 o C. Use the generlized compressiility chrt to estimte the totl propne mss nd to find the pressure. o use the generlized chrt we need the reduced pressure nd temperture so from le A.2 for propne c = 4250 k nd c = K. he reduced temperture is from Eq.3.8 r = c = = = From Figure D.1 shown elow we cn red for the sturted sttes Z = 0.78 r st por st liq. = 2.0 r = 0.7 r r st = 0.2, Z f = 0.035, Z g = ln r For the two-phse stte the pressure is the sturted pressure = r st c = k = 850 k he oerll compressiility fctor ecomes, s Eq.3.1 for Z = (1 x) Z f + x Z g = = he gs constnt from le A.5 is R = kj/kg K so the gs lw is Eq.3.7 diided y moleculr weight = mzr m = ZR = k m 3 = kj/kg kg

12 ONNAG/BORGNAKKE UDY ROBEM he computer tles Find the sttes in study prolems 3.2 nd 3.3 with the computer ided thermodynmics tles CA nd list the missing property of -- nd x if pplicle. Wter sttes from study prolem 3.2: Click t wter, click clcultor nd then select cse 1 (,). Input (, ) = (120, 0.5)

13 ONNAG/BORGNAKKE UDY ROBEM 3-12 Compressed liquid = m 3 /kg (sme s in le B.1.4) Click clcultor nd then select cse 2 (, ). Input (, ) = (120, 0.5) wo-phse x = , = k Ammoni stte from study prolem 3.3: Click t cryogenics, check tht it is mmoni otherwise select mmoni click clcultor nd then select cse 1 (,). Input (, ) = (30, 1) uperheted por = m 3 /kg (sme s in le B.2.2) R-22 stte from study prolem 3.3: Click t refrigernts, check tht it is R-22 otherwise select R-22 (lt-r) click clcultor nd then select cse 5 (, ). Input (, ) = (0.2, 0.15) uperheted por = o C

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