{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "Text" -1 211 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 219 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 } {CSTYLE "" -1 220 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE " " -1 221 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 222 " Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 223 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 224 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 225 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 226 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 227 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 } {CSTYLE "" -1 228 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE " " -1 229 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 230 " Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 232 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 233 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 234 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 235 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 236 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 } {CSTYLE "" -1 237 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE " " -1 238 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 256 " " 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE " " -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 2 0 2 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 2 0 2 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 16 0 0 0 1 2 1 2 2 2 2 1 1 1 1 } 1 1 0 0 8 2 2 0 2 0 2 2 0 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 2 0 2 0 2 2 0 1 }{PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 2 0 2 0 2 2 0 1 }{PSTYLE "No Name" -1 206 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 2 0 2 0 2 2 0 1 }{PSTYLE "No Name" -1 207 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 2 0 2 0 2 2 0 1 }{PSTYLE "No Name" -1 208 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 2 0 2 0 2 2 0 1 }{PSTYLE "No Name" -1 209 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 2 0 2 0 2 2 0 1 }{PSTYLE "No Name" -1 210 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 2 0 2 0 2 2 0 1 }{PSTYLE "Heading 1" -1 256 1 {CSTYLE "" -1 -1 "Times New Roman CE " 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 8 4 2 0 2 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 9 "FCH - A04" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 22 "I. termodynamick\341 v\354ta" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 40 "3.1.2 V\375po\350et entalpie u ide\341ln \355ho plynu" }}{PARA 0 "" 0 "" {TEXT 211 226 "Vnit\370n\355 energii a rgonu ve stavu ide\341ln\355ho plynu p\370i 25 \260C za tlaku 101,325 \+ kPa byla p\370isouzena hodnota 3718 J/mol. Jak\341 je odpov\355daj\355 c\355 hodnota mol\341rn\355 entalpie argonu? P\370edpokl\341dejte plat nost stavov\351 rovnice ide\341ln\355ho plynu. " }}{PARA 0 "" 0 "" {TEXT 211 12 "[6196 J/mol]" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart; " }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Vstupn\355 data" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "R:=8.314; T:=25+273; Um:=37 18;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "\330e\232en\355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 52 "3.1.3 V\375po\350et vnit\370n\355 energie l\341tky v kapaln\351m stav u" }}{PARA 0 "" 0 "" {TEXT 211 266 "Pro mol\341rn\355 entalpii kapaln \351ho methanolu p\370i 25 \260C a tlaku pst=101.325 kPa je mo\236no v literatu\370e nal\351zt hodnotu -234.280 kJ/mol. Vypo\350t\354te vnit \370n\355 energii kapaln\351ho methanolu (za uveden\375ch podm\355nek) , m\341-li methanol hustotu 0.791 g/cm3 a mol\341rn\355 hmotnost 32.03 g/mol." }}{PARA 0 "" 0 "" {TEXT 211 17 "[-234.284 kJ/mol]" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 1 {PARA 5 "" 0 " " {TEXT -1 12 "Vstupn\355 data" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "Hm:=-234.280e3; pst:=101.325e3; rho:=0.791e3; M:=32.03e-3; T:=25 +273.15;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "\330e\232en \355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 46 "3.1.4 Zm\354na vnit\370n\355 energie a en talpie u plynu" }}{PARA 0 "" 0 "" {TEXT 211 153 "Do autokl\341vu o obj emu 1 dm3 bylo dod\341no teplo Q=5000 J. P\370itom se zv\375\232ila te plota z 300 K na 400 K a tlak z 200 kPa na 250 kPa. Ur\350ete Delta U \+ a Delta H." }}{PARA 0 "" 0 "" {TEXT 211 28 "[DeltaU=5000 J, DeltaH=505 0]" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Vstupn\355 data" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Q:=5000; V:=1e-3; p1:=200e3; p2:=250e3; W:=0;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 " " {TEXT -1 6 "\330e\232en\355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 11 "Parn\355 stroj" }}{PARA 0 "" 0 "" {TEXT 211 288 "Ve v\341 lci pod p\355stem o pr\371\370ezu S=1 dm3 je uzav\370en 1 mol vodn\355 p\341ry o teplot\354 400 K. Na p\355stu je z\341va\236\355 m=100 kg, \+ p\355st se pohybuje bez t\370en\355. Atmosf\351rick\375 tlak je p=1 b ar. Dod\341n\355m tepla se zv\354t\232\355 objem syst\351mu tak, \236e dojde k posunu p\355stu sm\354rem vzh\371ru (proti gravita\350n\355mu poli) o l=1 cm. " }}{PARA 0 "" 0 "" {TEXT 219 2 "a)" }{TEXT 211 114 " Vypo\350t\354te objemovou pr\341ci plynu, u\236ite\350nou pr\341ci, k terou lze z\355skat pohybem z\341va\236\355, rozd\355l teplot a dodan \351 teplo." }}{PARA 0 "" 0 "" {TEXT 220 2 "b)" }{TEXT 211 86 " Kolik \+ procent z dodan\351ho tepla se p\370em\354nilo na pr\341ci plynu, koli k na u\236ite\350nou pr\341ci?" }}{PARA 0 "" 0 "" {TEXT 221 5 "Data:" }{TEXT 211 63 " Gravita\350n\355 zrychlen\355 je g=10 m.s-2, tepeln \341 kapacita Cpm=4*R. " }}{PARA 0 "" 0 "" {TEXT 211 44 "[W=-20 J, Wme ch=10 J, Delta T=2.4 K, Q=80 J]" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Vstupn\355 da ta" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "R:=8.314;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "S:=1e-2;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 5 "n:=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "T :=400;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "patm:=1e5;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "l:=0.01;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 6 "g:=10;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "m:=100;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "Cpm:=4*R; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "\330e\232en\355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 45 "3.1.8 V\375po\350et Q, W, U, H u izochorick\351ho d\354je" }}{PARA 0 "" 0 "" {TEXT 211 231 "V uzav\370en\351 n\341dob\354 o objemu V=50 dm3 jsou obsa\236eny dva moly ide\341ln\355ho jednoatomov\351ho plynu (CV m = (3/2)R) o teplot\354 25 \260C. N\341doba je oh\370\341ta na teplot u 125 \260C. Ur\350ete hodnoty Q, W, DeltaU, DeltaH a po\350\341te\350 n\355 a kone\350n\375 tlak v syst\351mu." }}{PARA 0 "" 0 "" {TEXT 211 37 "[DeltaU=Q=2494J, W=0, DeltaH=4157 J]" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart; " }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Vst upn\355 data" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "R:=8.314; V: =50e-3; CVm:=1.5*R; T1:=25+273.15; T2:=125+273.15; n:=2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "\330e\232en\355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 85 "3.1.1 V\375po \350et Q, W, U za konstantn\355ho tlaku ze z\341vislosti tepeln\351 ka pacity na teplot\354" }}{PARA 0 "" 0 "" {TEXT 211 125 "Mol\341rn\355 t epelnou kapacitu (v J/K/mol) vodn\355 p\341ry ve stavu ide\341ln\355ho plynu vystihuje v teplotn\355m intervalu 300 a\236 1000 K vztah" }} {PARA 0 "" 0 "" {TEXT 211 47 " Cpm = 31.63 + 5.083e-3 T + 4.597 e-6 T^2" }}{PARA 0 "" 0 "" {TEXT 211 35 "S pomoc\355 tohoto vztahu vyp o\350\355tejte:" }}{PARA 0 "" 0 "" {TEXT 222 2 "a)" }{TEXT 211 154 " t eplo Q, objemovou pr\341ci W, zm\354nu vnit\370n\355 energie U a zm \354nu entalpie H doprov\341zej\355c\355 oh\370\341t\355 1 mol p\341ry za tlaku 100 kPa z teploty 400 K na teplotu 600 K," }}{PARA 0 "" 0 " " {TEXT 223 2 "b)" }{TEXT 211 78 " st\370edn\355 mol\341rn\355 tepelno u kapacitu vodn\355 p\341ry pro interval teplot 400 a\236 600 K" }} {PARA 0 "" 0 "" {TEXT 211 71 "[Q=7067 J, DeltaU=5404 J, W=-1663 J, Cpm av[400,600]=35.34 J.K-1. mol-1]" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Vstupn\355 da ta" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "R:=8.314; T1:=400; T2: =600; n:=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Cpm := 31.63 + 5.083e-3*T + 4.597e-6*T^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "\330e\232en\355" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 "3.2.5+ V\375po\350et pr\341ce" }}{PARA 0 "" 0 "" {TEXT 211 136 "Vypo \350t\354te pr\341ci pot\370ebnou k izotermick\351mu vratn\351mu stla \350en\355 p\354ti mol\371 oxidu uhli\350it\351ho p\370i 40 \260C z tl aku 0.1 MPa na tlak 3 MPa. Pou\236ijte" }}{PARA 0 "" 0 "" {TEXT 224 2 "a)" }{TEXT 211 34 " stavovou rovnici ide\341ln\355ho plynu," }}{PARA 0 "" 0 "" {TEXT 225 2 "b)" }{TEXT 211 60 " viri\341lovou stavovou rovn ici ve tvaru (Vm je mol\341rn\355 objem) " }}{PARA 0 "" 0 "" {TEXT 211 25 " p Vm = R T + B p" }}{PARA 0 "" 0 "" {TEXT 211 52 " \+ s druh\375m viri\341lov\375m koeficientem B = 98 cm3/mol," }}{PARA 0 "" 0 "" {TEXT 226 2 "c)" }{TEXT 211 54 " van der Waalsovu rovnici (Tc= 304.17 K, pc=7.386 MPa)." }}{PARA 0 "" 0 "" {TEXT 211 33 "[Wid=Wvir=44 276 J, WvdW=44278 J] " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "rest art;" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Vstupn\355 data" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "R:=8.314;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "B:=-98e-6;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Tc:=304.17;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "pc:=7.386e6;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "p1:=0 .1e6; p2:=3e6;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "T:=273.15 +40;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "n:=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "\330e\232en\355" }}{SECT 1 {PARA 20 "" 0 "" {TEXT -1 34 "a) stavov\341 rovnice ide\341ln\355ho pl ynu" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 20 "" 0 "" {TEXT -1 29 "b) viri\341lov\341 stavov\341 rovnice " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 20 "" 0 "" {TEXT -1 27 "c) van der Waalsova rovnice" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 22 "V\375po\350et \+ pr\341ce graficky" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 227 2 "a)" }{TEXT 211 91 " Expanze plynu \+ prob\355hala v p=V diagramu po p\370\355mce podle obr\341zku. Vypo\350 t\354te vykonanou pr\341ci." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "pol ygonplot([[0.1,0],[0.1,2],[0.2,1],[0.2,0]],color=green,view=[0 .. 0.3, 0 .. 2.5],labels=[\"V/m3\",\"pvn/bar\"]);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 25 "W=-(0.2-0.1)*(2e5+1e5)/2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 228 2 "b)" } {TEXT 211 108 " Cyklick\375 d\354j prob\355hal ve sm\354ru hodinov\375 ch ru\350i\350ek podle obr\341zku. Vypo\350t\354te vykonanou pr\341ci \+ na jeden cyklus." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "polygonplot([[ 0.1,1],[0.1,2],[0.2,1],[0.2,0.5]],color=green,view=[0 .. 0.3, 0 .. 2.5 ],labels=[\"V/m3\",\"pvn/bar\"]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "W=-( (0.2-0.1)*1.5e5-(0.2-0.1)*0.75e5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 15 "Adiabatick\375 d\354j" }{TEXT 211 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 37 "Poissonova konstanta a rychlost zvuku" }}{PARA 0 "" 0 "" {TEXT 211 60 "Rychlost zvuku v oxidu uhli\350it\351m za teplot y 25 \260C je 270 m/s" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT 229 2 " a)" }{TEXT -1 61 " Jak\341 je jeho mol\341rn\355 tepeln\341 kapacita z a konstantn\355ho tlaku?" }}{PARA 0 "" 0 "" {TEXT 230 2 "b)" }{TEXT -1 128 " *Je-li rychlost zm\354\370ena s p\370esnost\355 +- 0.5 m/s, s jakou p\370esnost\355 je stanovena Poissonova konstanta a s jakou tep eln\341 kapacita?" }}{PARA 0 "" 0 "" {TEXT -1 48 "N\341vod: pro rychlo st zvuku v ide\341ln\355m plynu plat\355" }}{PARA 0 "" 0 "" {TEXT -1 23 " v^2=kappa R T/M" }}{PARA 0 "" 0 "" {TEXT -1 14 "[36.6 J/K/ mol]" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Vstupn\355 data" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "T:=298.15;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "R:=8.314;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "M:=(12+ 2*16)*1e-3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "v:=270; # a \+ napodruhe prepocteme s v:=270.5 ==> chyba" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "\330e\232en\355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "Poissonovy rovnice" } }{PARA 0 "" 0 "" {TEXT 211 199 "Podle \372daj\371 v\375robce m\341 b \375t pneumatika auta nahu\232t\354na na tlak 200 kPa. Na jakou teplot u se zah\370eje vzduch v hustilce? Atmosf\351rick\375 tlak je 100 kPa, teplota 25 \260C. Poissonova konstanta vzduchu je 1.4." }}{PARA 0 " " 0 "" {TEXT 211 8 "[135 \260C]" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Vstupn\355 da ta" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "R:=8.314; kappa:=1.4; \+ p1:=100; T1:=273+25;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "\330e\232en\355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 6 "Diesel" }}{PARA 206 "" 0 "" {TEXT 211 154 "Do vzn\354tov\351ho motoru (kompresn\355 pom\354r 18, zdvihov\375 obj em 500 cm3) se nas\341v\341 se vzduch o atmosf\351rick\351m tlaku 1 ba r p\370edeh\370\341t\375 na teplotu 350 K. Vypo\350t\354te: " }}{PARA 207 "" 0 "" {TEXT 232 2 "a)" }{TEXT 211 52 " teplotu a tlak vzduchu po stla\350en\355 [1112 K, 57 bar]" }}{PARA 208 "" 0 "" {TEXT 233 2 "b) " }{TEXT 211 53 " objemovou pr\341ci vykonanou p\370i stla\350en\355 p lynu [288 J]" }}{PARA 209 "" 0 "" {TEXT 234 2 "c)" }{TEXT 211 81 " mec hanickou pr\341ci, kterou je nutno dodat na stla\350en\355 (t\370en \355 zanedb\341v\341me) [238 J]" }}{PARA 210 "" 0 "" {TEXT 211 36 "Poi ssonova konstanta vzduchu je 1.4." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Vstu pn\355 data" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "z:=18; p1:=10 0e3; T1:=350; kappa:=1.4; R:=8.314; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 211 15 "Zdvihov\375 objem:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Vzd:= 500e-6;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "\330e\232en\355" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 46 "*Experiment\341ln\355 stanoven\355 Poissonovy konstanty" }}{PARA 0 "" 0 "" {TEXT 211 406 "T lakom\354r na \236elezn\351 dob\370e uzaw\370en\351 a uwnit\370 plstj \+ dob\370e wylo\236en\351 n\341dob\354 s nezn\341m\375m plynem ukazuge 7 43 mm Hg. Tlak pow\354t\370j gest 760 mm Hg a teplota 20 \260R. Went il byl rychle otew\370en. Kdy\236 plyn p\370estal sy\350eti a tlakom \354r uk\341zal 0 mm Hg, byl wentil zase ztuha uzaw\370en. Tjm n\341d oba se ochladila. Po n\354kolika hodin\341ch vyrovnaly se teploty, tl akom\354r uk\341zaw 143.6 mm Hg. Kolik gest Poissonowa konstanta? [1. 34]\n" }}{PARA 0 "" 0 "" {TEXT 211 91 "Jedn\341 se o historickou metod u -- nyn\355 se Poissonova konstanta stanovuje z rychlosti zvuku.\n" } }{PARA 0 "" 0 "" {TEXT 211 422 "Jev m\371\236ete s trochou \232ikovnos ti pozorovat na nafouknut\351 pneumatice: Co nejv\355c nafouknout, nec hat vyrovnat teploty, co nejrychleji vypustit, okam\236it\354 zm\354 \370it tlak, po\350kat na vyrovn\341n\355 teplot (sta\350\355 chv\355l i -- tepeln\341 kapacita pneumatiky je mnohem v\354t\232\355 ne\236 vz duchu) a zm\354\370it tlak znovu. Nam\354\370\355te o n\354co v\355c, \+ ale teoretickou hodnotu nedos\341hnete, proto\236e vypou\232t\354n\355 je pomal\351 a vzduch se oh\370\355v\341 od pneumatiky b\354hem vypou \232t\354n\355. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart; " }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Vstupn\355 data" }}{EXCHG {PARA 0 "" 0 "" {TEXT 211 53 "Podle definice 760 mm Hg = 760 torr = ps t = 101325 Pa" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "torr:=10325./760; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "p2:=760*torr;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "p1:=743*torr+p2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 211 14 "80 \260R = 100 \260C" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 21 "T1:=273.15+20*100/80;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "\330e\232en\355" }}{EXCHG {PARA 0 "" 0 "" {TEXT 211 56 "kappa nezn\341m, ale to mi nevad\355. Jen kv\371li po\370\341 dku p\355\232u " }{TEXT 235 5 "T2vyr" }{TEXT 211 7 " m\355sto " } {TEXT 236 2 "T2" }{TEXT 211 68 ", abych v\354d\354l, \236e to nen\355 \+ \350\355slo. Teplota po expanzi je (plat\355 T2 " 0 "" {MPLTEXT 1 0 30 "T2vyr:=T1*(p1/p2)^(1/kappa-1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 211 84 "Tlak po vzr\371stu teploty z T2 zp\354t na T1; v \232imn\354te si, \236e tam st\341le m\341m nezn\341m\351 kappa" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p3vyr:=p2*(T1/T2vyr);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 211 52 "A to se m\341 rovnat (p2=atm. tlak, 143. 6*torr=p\370etlak)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "p3:=p2+143.6* torr;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 211 16 "A te\357 to vy\370e\232 \355m" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "fsolve(p3vyr=p3,kappa);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 24 "Nevratn\375 adiabatic k\375 d\354j" }}{PARA 0 "" 0 "" {TEXT 211 69 "Jeden mol vzduchu (Cpm=3 .5 R) o teplot\354 400 K a tlaku 2 bar expanduje" }}{PARA 0 "" 0 "" {TEXT 237 2 "a)" }{TEXT 211 19 " vratn\354 adiabaticky" }}{PARA 0 "" 0 "" {TEXT 238 2 "b)" }{TEXT 211 88 " nevratn\354 proti st\341l\351mu \+ vn\354j\232\355mu tlaku 1 bar a\236 se tlak vyrovn\341 s atmosf\351ric k\375m (1 bar)." }}{PARA 0 "" 0 "" {TEXT 211 62 "Vypo\350t\354te vykon anou pr\341ci a koncovou teplotu v obou p\370\355padech." }}{PARA 0 " " 0 "" {TEXT 211 24 "[a) -1494 J, b) -1188 J]" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart; " }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Vstupn\355 data" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "R:=8. 314; p1:=2e5; p2:=1e5; T1:=400; n:=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Cpm:=3.5*R;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "\330e\232 en\355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}}} {MARK "2" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }