.MCAD 310000000 \  docDocument MmcObject[22 d2_graph_format graphData% axisFormat)L)Ltrace2D&&&&&&&&& & & & & &&& dim_formatTmasslengthtimecharge temperature luminosity substanceNumericalFormatQdii  shpRectVs1mcDocumentObjectState\ mcPageModelKw>_>L?}G?mcHeaderFooterI|F|P|D@I  CHeaderFooterJ{f}{n}{d}@J@J@J MbP?MbP? TextState? TextStyle>@ Arial Rounded MT BoldSerial_ParPropDefaultW?Normalfont_style_listO font_styleP  VariablesTimes New Roman@P  ConstantsTimes New Roman@P TextArial Rounded MT Bold@P Greek VariablesSymbol@P User^1Arial@P User^2 Courier New@P User^3System@P User^4Script@P User^5Roman@P User^6Modern@P User^7Times New Roman@P SymbolsSymbol@P Current Selection FontArial@P Undefined Font@P HeaderTimes New Roman@P FooterArial@P Rotated Math FontTimes New Romanb TextRegion* docRegionGshpBoxU A-99$9$ CharacterMap-RangeMap;@yRotational specific heat of para-H2, ortho-H2, high temperature mixture, and equilibrium mixture of the two modifications ChrPropMap7-!y RangeElem<!  ChrPropData8 RangeData=l Verdana < 8| Verdana < 8\ Verdana < 8l Verdana <8L Verdana8<?<@@8<^=@A<@B8<?@A?9@C<@D:@W,1@E</@F<@G0@NormalArial Rounded MT Bold @H@B@UL#]X@I@@ p@J@@ @I@K@@d@JB@L@@@J5932.2@M@B@U@TmNh@N@@ p@O@@@N@P@@d@Oh@Q@@@O@R@@t@Q  6.6260755@S@@@Q@T@@t@S10@U@@K@S@V@@@U34@W*@U\kh&-[J s]79@X<@Y:@W,1@Z</@[<@\0@NormalArial Rounded MT Bold @]*@Udsp-(seeVP_OH2.mcd)79@^<@_:@W,1@`</@a<@b0@NormalArial Rounded MT Bold @c@B@Uc&x @d@@ p@e@@ @d@f@@d@e\qr@g@@@e@h@@@@g@i@@@@h@j@@d@ih@k@@@ic@l@@@hB@m@@@gk@n@B@U@tM @o@@ p@p@@@o@q@@d@pk@r@@@p@s@@t@r 1.380658@t@@@r@u@@t@t10@v@@K@t@w@@@v23@x*@Uy 4&&-[J K-1]7@y<@z8@x@{<@|8@x^@y@}<@~8@x@{@}@{9@<@:@W,1@</@<@0@NormalArial Rounded MT Bold @*@U- Rotational temperature of H2 [K]7 @<@8@@<@8@^@@<@8@@@@9 @< @:@W?1@</ @< @0@NormalArial Rounded MT Bold @@B@U,@@@ p@@@@@@@d@\qr@@@@@@@+@@Serial_DisplayNodeX@@@@ _n_u_l_l_@@B@U@M@@@ p@@@@@@@d@c@@@@@@@t@  2.99792458@@@@@@@t@10@@@@8@*@U4((-[m s-1]7@<@8@@<@8@^@@<@8@@@@9@<@:@W,1@</@<@0@NormalArial Rounded MT Bold @@B@U@P@@@ p@@@@@@@d@R@@@@  1.9872156@*@UnVV-[cal mol-1 K-1]7@<@8@@<@8@^@@<@8@@@<@8@^@@<@8@@@@9@<@:@W,1@</@<@0@NormalArial Rounded MT Bold @*@U-H has nuclear spin 1/2 h/2p7@<@8@@<@8@Symbol@@@9@<@:@W,1@</@<@0@NormalArial Rounded MT Bold @*@U-"Rotational partition function for:7"9"@<"@:@W,1@</"@<"@0@NormalArial Rounded MT Bold @@B@U?@@@ p@@@ @@@@d@i@@@@@@@t@0@@@@800@@B@U@@@ p@@@ @@@@@@@@@d@T@@@@i@@@@@@@@@@@@t@0.5@@@@i@@@@1@*@U  -[K]79@<@:@W,1@</@<@0@NormalArial Rounded MT Bold @*@U)-Temperature vector79@<@:@W,1@</@<@0@NormalArial Rounded MT Bold @*@U+(-Index of quantum numbers:79@<@:@W,1@</@<@0@NormalArial Rounded MT Bold @@B@U4-(@@@ p@@@ @@@@d@j@@@@@@@t@0@@@@5@*@UX +X(-corresponds to J = 0 to 1179@<@:@W1@</A<A0@NormalArial Rounded MT Bold A*@U4qC@iii-@SWe first compute the thermal ortho-para equilibrium; the common energy base is J=0:7S9SA@@A<iA?@@A9A@@@p@A?AA@@A@AB@@@AAAC@@tAB4AD@@ABjAE@@AA3AF@@A?AG@@dAFexpAH@@pAFAI@@AHAJ@@@AIAK@@K@AJAL@@pAKAM@@ALAN@@@AMAO@@tAN2AP@@ANjAQ@@AM1AR@@pAJAS@@ARAT@@@ASAU@@tAT2AV@@ATjAW@@AS2AX@@AIAY@@dAX\qrAZ@@AXA[@@dAZTA\@@AZiA]*@U0K0!!-@APopulation matrix o-H2 J = 1,3,5,7,9,11,... only odd J's allowed7AA^<A_8A]A`<Aa8A]^A^Ab<+Ac8A]A`AbA`9AAd<;B?8B=B@<BA8B=^B>BB<BC8B=B@BBB@9=BD<=BE:@W,1BF</=BG<=BH0@NormalArial Rounded MT Bold BI*@U(C(X-p-H27BJ<BK8BIBL<BM8BI^BJBLBL9BN<BO:@W,1BP</BQ<BR0@NormalArial Rounded MT Bold BS@B@U70BT@@ pBU@@ BTBV@@@BUBW@@dBVdlnQpBX@@BVkBY@@BUBZ@@@BYB[@@dBZlnQpB\@@BZB]@@dB\kB^@@B\1B_@@BYB`@@dB_lnQpBa@@B_kBb@B@Uv1Bc@@ pBd@@ BcBe@@@BdBf@@dBedlnQoBg@@BekBh@@BdBi@@@BhBj@@dBilnQoBk@@BiBl@@dBkkBm@@Bk1Bn@@BhBo@@dBnlnQoBp@@BnkBq*@UMEE-5Rotational specific heat Cp per Mol for p- and o-H2:7435Br<3Bs8BqBt<Bu8Bq^BrBv<Bw8BqBtBvBt95Bx<5By:@W,1Bz</5B{<5B|0@NormalArial Rounded MT Bold B}@B@U <10B~@@ pB@@ B~B@@@BB@@dBppB@@BlB@@BB@@@BB@@tB4B@@BRB@@pBB@@BB@@@BB@@@BB@@p@BB@@BB@@dBTB@@BB@@dBlB@@B1B@@B2B@@BB@@dBdlnQpB@@BB@@dBlB@@B1B@@BB@@@BB@@p@BB@@BB@@dBTB@@BlB@@B2B@@BB@@dBdlnQpB@@BlB@B@UL l1`B@@ pB@@ BB@@@BB@@dBpoB@@BlB@@BB@@@BB@@tB4B@@BRB@@pBB@@BB@@@BB@@@BB@@p@BB@@BB@@dBTB@@BB@@dBlB@@B1B@@B2B@@BB@@dBdlnQoB@@BB@@dBlB@@B1B@@BB@@@BB@@p@BB@@BB@@dBTB@@BlB@@B2B@@BB@@dBdlnQoB@@BlB*@U(TCf(`P-o-H27B<B8BB<B8B^BBB9B<B:@W,1B</B<B0@NormalArial Rounded MT Bold B@B@U| 7B@@ pB@@ BB@@dBpmB@@BB@@@BB@@tB0.25B@@BppB@@BB@@tB0.75B@@BpoB*@U|8!!-@F'frozen' high temperature mixture of p-H2/o-H2 = 1/3, normal hydrogen7.(FB<B8BB<B8BBB<B8BBB<B8B^BB<B8BBB<B8B^BB<B8BBBB9FBC0@@ pC1@@ C0C2@@dC1\eC3@@C1C4@@@C3C5@@@C4C6@@dC5BC7@@C5hC8@@C4cC9@@C3C:@@dC9NaC;@@C94.184C<*@U1C@?QAA- [cal mol-1]7  C=<C>8C<C?<C@8C<^C=CA<CB8C<C?CAC?9 CC< CD:@W,1CE</ CF< CG0@NormalArial Rounded MT Bold CH*@U<KH~-!Data vectors of Clusius & Hiller:7!9!CI@@ pD?@@ D>D@@@dD?yccDA@@pD?DB@@0DADC@@0ADBDD@@0ADCDE@@0ADDDF@@0ADEDG@@0ADFDH@@0ADGDI@@0ADHDJ@@0ADIDK@@0ADJDL@@0ADKDM@@0ADLDN@@0ADMDO@@0ADNDP@@@DODQ@@DO2.792DR@@DN2.629DS@@DM2.714DT@@DL2.57DU@@DK2.457DV@@DJ2.342DW@@DI2.286DX@@DH2.118DY@@DG1.836DZ@@DF1.675D[@@DE1.443D\@@DD1.203D]@@DC1.037D^@@DB0.897D_@B@U,! ID`@@ pDa@@ D`Db@@@DaDc@@dDbpgDd@@DblDe@@DaDf@@@DeDg@@@DfDh@@p@DgDi@@DhDj@@tDi1Dk@@DiDl@@dDkxDm@@DklDn@@DgDo@@dDnppDp@@DnlDq@@DfDr@@@DqDs@@dDrxDt@@DrlDu@@DqDv@@dDupoDw@@DulDx@@DeDy@@dDxzDz@@DxlD{*@U& J-$Cpg for equilibrium o-/p-H2 mixture7$D|<D}8D{D~<D8D{^D|D<D8D{D~DD~9$D<$D:@W,1D</$D<$D0@NormalArial Rounded MT Bold D@B@U41L@D@@ pD@@ DD@@@DD@@dDhtD@@DlD@@DRD*@U4C@-*asymptote for all Cp's at high temperature7*9*D<*D:@W,1D</*D<*D0@NormalArial Rounded MT Bold D@B@UL6]X{D@@ pD@@ DD@@dDxcD@@DxccD@B@UhL]}XzD@@ pD@@ DD@@dDycD@@DyccD@B@UL]XD@@ pD@@ DD@@dDmD@@DD@@tD0D@@D13D*@U L[ X-data vectors on right page ->79D<D:@W1D</D<D0@NormalArial Rounded MT Bold D*@UdevpQ]]]-@Zcrosses are 14 datapoints from K.Clusius & K.Hiller, Z.Phys.Chem. B4(1929)158 for 95% p-H27YBZD< D8DD<6D8DDD<D8D}DD<D8DDD<D8D^DDD9ZD@2D@@ pD@@DD@@@DD@@@DD@@@DD@@tD4.5D@@D0D@@DD@@tD0D@@D4.5D@@ DD@@ @DD@@ @DD@@ @DD@@ @DD@@ @DD@@ @DD@@ @DD@@dDRD@@DD@@dDpgD@@DlD@@DD@@dDppD@@DlD@@DD@@dDpmD@@DlD@@DD@@dDpcD@@DlD@@DD@@dDpoD@@DlD@@DD@@dDzD@@DlD@@DD@@dDxpD@@DlD@@DD@@dDycD@@DmD@@DD@@@DD@@@DD@@tD400D@@D0E@@DE@@tE0E@@E320E@@ DE@@ @EE@@ @EE@@ @EE@@ @EE@@ @EE @@ @EE @@ @E E @@@E E @@dE TE @@E lE@@E E@@dETE@@ElE@@E E@@dETE@@ElE@@EE@@dETE@@ElE@@EE@@dETE@@ElE@@EE@@dETE@@ElE@@EE@@dETE@@ElE @@EE!@@dE TE"@@E lE#@@EE$@@dE#xcE%@@E#mE& /. )N)F&&&&&&&&&& & & & & &&&E'*@Uh-Cpg79E(<E):@W,1E*</E+<E,0@NormalArial Rounded MT Bold E-*@U"# h-Cpp79E.<E/:@W,1E0</E1<E20@NormalArial Rounded MT Bold E3*@UD2SPh-Cpc79E4<E5:@W,1E6</E7<E80@NormalArial Rounded MT Bold E9*@U|c-z79E:<E;:@W1E<</E=<E>0@NormalArial Rounded MT Bold E?*@UHbH.h-Cpo79E@<EA:@W,1EB</EC<ED0@NormalArial Rounded MT Bold EE*@U-h-Cpm79EF<EG:@W,1EH</EI<EJ0@NormalArial Rounded MT Bold EK*@U/-"fraction of para-H2 in equilibrium7"9"EL<"EM:@W1EN</"EO<"EP0@NormalArial Rounded MT Bold EQ*@U`Db`P+-@[From left to right: Cpg equilibrium, z, Cpp, datapoints, Cpc, Cpm normal hydrogen, and Cpo.7[9[ER<[ES:@W?1ET</[EU<[EV0@NormalArial Rounded MT Bold