Gases, Ideal Gas Law 5 | HP 48gII Graphing, 50g Graphing instruction

Gases (5)

Variable

Description

λMean free path

ρFlow density

ρ0	Stagnation density

AFlow area

At	Throat area

dMolecular diameter

kSpecific heat ratio

MMach number

mMass

MW	Molecular weight

nNumber of moles, or

Polytropic constant (Polytropic Processes)

PPressure, or Flow pressure (Isentropic Flow)

P0	Stagnation pressure
Pc	Pseudocritical pressure
Pi, Pf	Initial and final pressures

TTemperature, or Flow temperature (Isentropic Flow)

T0	Stagnation temperature
Tc	Pseudocritical temperature
Ti, Tf	Initial and final temperature

VVolume

Vi, Vf	Initial and final volumes
vrms	Rootmeansquare (rms) velocity

WWork

References:1, 3.

Ideal Gas Law (5, 1)

Equations:

P ⋅ V = n ⋅ R ⋅ T

m = n ⋅ MW

Equation Reference 525

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Image 461

HP 48gII Graphing, 50g Graphing manual Gases, Ideal Gas Law 5

Contents

Advanced user’s reference manual HP 50g / 49g+ / 48gII graphing calculatorPage Printing History AcknowledgementsPage Contents Algb NamesAlog Amort 317 Delay Delalarm→COL COL→ 359 EXP2POW FindalarmExpan Expand IBP HaltIDIV2 Iferr List Maxr MAXMIN Not Parametric PA2B2Parity Parsurface 3183 Rnrm RNDRoll Rolld 3226 →TAG TabvarTail TAN Updir WireframeUtpc Utpf Contents 514 →ALG Apeek ARM→ ASM ASM→ 610 CST Exited Expr Iopar MASD.INI AlrmdatToff Tpar Vpar Understanding Programming Contents of a Program Program Results Calculations in a ProgramExamples of Program Actions Entering and Executing Programs To enter commands and other objects in a programTo enter a program To store or name a program 3Q!Ì*4`3/*@Ï To stop an executing program3Q!Ì*4#3/* @Ë@Ï @% @Ér # O4 /3 *!Ì Q3 @Ë@Ï Osph K LevelProgram Keys Comments Viewing and Editing Programs To switch between entry modesTo view or edit a program @%SPH% ˜ Creating Programs on a Computer Using Local VariablesCreating Local Variables `J!%SPH% @%SPH% ˜ `OSPHLV K Program Comments Defining the Scope of Local Variables Evaluating Local Names Creating UserDefined Functions as Programs Compiled Local Variables Testing Conditions Using Tests and Conditional StructuresKey Programmable Description Command To include a test in a program Keys Programmable Description Command Using Logical FunctionsLogical Functions TEST% L To enter if then END in a program Using Conditional Structures and CommandsPress !%BRCH% !%IF% To enter IFT in a program Press !%BRCH% @%#IF#% To enter if then Else END in a programTo enter Ifte in a program or in an algebraic Press !%BRCH% L!%IFTE% Conditional Examples To enter Case END in a program 26 `52 J %TST% Otst K While … Repeat … END Using Loop StructuresUsing Definite Loop Structures « … start finish Start loopclause Next … » Start Next StructureTo enter Start Next in a program Press !%BRCH% !%START% « … start finish Start loopclause increment Step … » Start Step StructureTo enter Start Step in a program Press ! %BRCH% … %START% « … start finish for counter loopclause Next … » For Next StructureTo enter for Next in a program Press !%BRCH% ! %FOR% « … start finish for counter loopclause increment Step … » For Step StructureTo enter for Step in a program Press ! %BRCH% … %FOR% Do Until END Structure Using Indefinite Loop Structures« … do loopclause Until testclause END … » To enter do Until END in a program Duplicates n, stores the value into n « … While testclause Repeat loopclause END … » While Repeat END StructureTo enter While Repeat END in a program Press !%BRCH% ! %WHILE% Press ! #MEM# %ARITH% %INCR% or %DECR% Using Loop CountersTo enter Incr or Decr in a program ∑ j Using Summations Instead of Loops Setting, Clearing, and Testing Flags Using FlagsTypes of Flags To set, clear, or test a flag Example Recalling and Storing the Flag StatesMonth/day/year format Day.month.year format To recall the current flag states Using SubroutinesExecute Rclf !L %MODES% %FLAG% L%RCLF% To change the current flag states ` 8 J %TORSV% Torsa KTorsv K To turn off the Halt annunciator at any time To singlestep from the start of a programPress !LL %RUN% %KILL% @·J6 `8 `O%TORSV% !LL%RUN% %DBUG% @·J10 `12 O%TORSV% !LL%RUN% %DBUG% To singlestep when the next step is a subroutineTo singlestep from the middle of a program Causing and Analyzing Errors Trapping ErrorsTo cause a userdefined error to occur in a program SingleStep Operations To analyze an error in a program To artificially cause a builtin error to occur in a programError Trapping Commands %ERROR% « … Iferr trapclause then errorclause END … » Making an Error TrapPress !LL %ERROR% !%IFERR% Iferr then END Structure To enter Iferr then Else END in a program Press !LL %ERROR% @%IFERR%Iferr then Else END Structure Using PROMPT, Cont for Input Data Input CommandsKey Command Description Input @·J %TPROM% `OTPROMPT ‰ To respond to Halt while running a program Using Disp Freeze HALT, Cont for InputTo enter Disp Freeze Halt in a program « … promptstring commandline Input OBJ→ … » Using INPUT, Enter for InputTo enter Input in a program To respond to Input while running a program %VSPH% To design the commandline string for Input Commandline cursorposition operatingoptionsTo include Input options Cursorposition `O Tinput ‰ To process the result string from InputPress @ Õ ! Ê a @ %TINPU% To set up an input form Using Inform and Choose for Input To set up a choose box `OPHONES ‰ Beeping to Get Attention Using Wait for Keystroke InputTo enter Beep in a program To enter Wait in a program Data Output Commands Using KEY for Keystroke InputOutput OUT% Labeling and Displaying Output as Strings Labeling Output with TagsTo label a result with a tag %TTAG% 1.5 ˜1.85 ` Using Msgbox to Display Output Pausing to Display OutputTo set up a message box `OTSTRING ‰ Using Menus for Input Using Menus with Programs To create a menubased application Using Menus to Run ProgramsOlst ‰ SI% @·J%EIZ% %% !Ü.37~@6 68 %%I%% !%%Z%% Turning Off the Calculator from a Program@%%I%% 2*%%I%% !%%E%% To turn off the calculator in a programPage RPL Programming Examples Fibonacci NumbersFIB1 Fibonacci Numbers, Recursive Version FIB1% !Ü10 N FIB2 Fibonacci Numbers, Loop Version%FIB1% 10 %FIB2% FIB2 program listing%FIB2% Techniques used in Fibt Fibt Comparing ProgramExecution TimeStructured programming. Fibt calls both FIB1 and FIB2 Required Programs PAD Pad with Leading Spaces Displaying a Binary Integer13 %FIBT% Techniques used in PAD PAD program listing Preserve Save and Restore Previous Status`OPAD K Techniques used in Preserve `OPRESERVE K Bdisp Binary DisplayPreserve program listing PAD Techniques used in Bdisp `OBDISP K Bdisp program listing 144 %BDISP% Median of Statistics DataTile Percentile of a list Techniques used in %TILE Median Median of Statistics DataTile program listing `O%TILE K Required Program Techniques used in Median `OMEDIAN K Expanding and Collecting Completely18 `12 `˜šš 11 `1 ` Techniques used in Multi Multi Multiple ExecutionMulti program listing `OMULTI K Techniques used in Exco Exco Expand and Collect CompletelyExco program listing `OEXCO K MNX Minimum or Maximum Element-Version Minimum and Maximum Array ElementsÜ4 *Y+Z + User and system flags for logic control `OMNX K MNX program listing Techniques used in MNX2 MNX2 Minimum or Maximum Element-Version12 `56 `˜šš 45 `1 ` MNX2 program listing %MNX2% Applying a Program to an ArrayTechniques used in Aply Aply program listing Make sure the flag 1 is clear to begin `OAPLY K Converting Between Number BasesÔ3†2W†4` ‚Å 3 QA *7 `J %APLY% H#DISP ˜˜ Techniques used in nBASE NBASE program listing 1000 `23 J %NBASE% Verifying Program Arguments Techniques used in Names Names Check List for Exactly Two NamesNames program listing `ONAMES K VFY program listing VFY Verify Program ArgumentTechniques used in VFY Oben ` Converting Procedures from Algebraic to RPNOjeff ` Osarah ` %LIST% %²LIST% →RPN program listing Techniques used in →RPN Techniques used in BER Bessel FunctionsXQ3 `%²RPN% `OBER K BER program listing%BER% %BER% !Ü2 Sintp Converting a Plot to a Graphics Object Animation of Successive Taylor’s PolynomialsTechniques used in Sintp Sintp program listing Techniques used in Setts Setts Superimposing Taylor’s polynomialsSetts program listing `OSETTS K Techniques used in TSA TSA Animating Taylor’s PolynomialsTSA program listing `OTSA K Programmatic Use of Statistics and Plotting Programmatic use of matrices and statistics commandsTechniques used in PIE Temporary menu for data input Angle 983 %SLICE% 416 %SLICE% 85 %SLICE% `OPIE K Techniques used in αENTER and ßENTER Trace ModeΑENTER program listing ßENTER program listing Techniques used in Rootr InverseFunction SolverRootr program listing `OROOTR K @Å@É x †O3.7 Animating a Graphical Image%X²FX% ` 599.5 ` 1 %ROOTR% Techniques used in Walk `OWALK K Acos IntroductionType Input/Output Parallel Processing with Lists How Commands Are AlphabetizedOther Provided Details Classification of Operations Computer Algebra System Commands and Functions Realnumber time or angle in hoursminutessecond s format Backup identifierLibrary identifier Binary integer ACK AbcuvABS Type Description Ackall ASIN, ATAN, COS, Isol ACOS2S ASIN2C, ASIN2T, ATAN2S AcoshAcosh z Symb ACOSHsymb Addtmod ADD Algb AddtorealAlog 10z TVM, TVMBEG, TVMEND, Tvmroot AmortPrincipal Interest Balance ANS Animate ARC Access …µAPPLY Input/OutputApply ARG Archive Arit Access …µARRY→ Input/OutputARRY→ →ARRY Access !¼ ¼is the leftshift of the Skey Asinh ASIN2CASIN2T Asinh z ASNSymb ASINHsymb ACOSH, ATANH, ISOL, Sinh ASR Access … ÃL BIT ASRAssume Skey ADDTOREAL, Unassume Atan Atan z ATAN2SSymb ATANsymb ACOS, ASIN, ISOL, TAN Atanh Access …µATICKAtick Atanh z Attach Access …µATTACH Input/OutputAugment #n #m Auto Access …µAUTO Input/Output NoneAxes BAR AXL Access …µAXES Input/OutputAXM Atick xaxis label yaxis label BAR AXQAXL, AXQ AXL, AXM, GAUSS, QXA Barplot Access …µBAR Input/Output NoneBasis Baud Access … Ã BIN Access …µBESTFIT Input/Output NoneBeep Bestfit Bins Access !L Pict BOX Is the leftshift of the NkeyBlank BOX Buflen Access …µBUFLEN Input/OutputBytes #n1 #m1 #n2 #m2 X1, y1 X2, y2 Cascfg Access … Ã B → RC2P Help CascmdCase Centr CeilXunit Nunit Symb CEILsymb FLOOR, IP, RND, Trnc Cholesky Chinrem CHR Command ResultChoose Cksm CircNUM, POS REPL, SIZE, SUB Clkadj ClearCllcd Closeio Clusr CLΣClvar Cmplx COL →COLCOL→ Colct COL+Collect Symb1 Symb2 Comb ColσCON Symb COMBsymb ,m COMBn, symb COMBsymb ,symb Rarray constant CondCarray constant Name IDN Conj Access …µCONIC Input/Output NoneConic Const ConlibConstants Rarray Carray Symb CONJsymb Convert ContCorr X1unitssource X2unitstarget X3unitstarget COS Access FlagsCosh COV Cross CrdirCswp …µCR Cyclotomic CurlCylin COL+, COL-, Rswp Darcy →PXDate #n, #m DATE+ →DATEDbug →date DEC DdaysDecr « program » or program name DEF DedicaceDefine Result See also DEG DelalarmDegree Name=exp Namename Name =expname RCLALARM, Stoalarm DelayDelkeys CR, OLDPRT, PRLCD, PRST, PRSTC, PRVAR, PR1 Depnd Access …µDEPND Input/OutputDepth Xkey1, ... ,xkey n Desolve DerivDervx DET Access …µDETACH Input/OutputDetach Attach Diagmap DIAG→→DIAG Diffeq Diff Disp Access …µDIFFEQ Input/OutputDIR Distrib DispxyObj List FREEZE, HALT, INPUT, Prompt DIV2 DIVDIV2MOD CURL, Hess Divmod DivisDivpc DIV2 DERIV, DERVX, DESOLVE, ∂ TAYLOR0, TAYLR, SeriesUntil testclause END END Dolist ErrorDoerr Domain List List n « program » Results Command Name List n+1Dosubs SIGNTAB, Tabvar DOT List « program » Command NameDOLIST, ENDSUB, NSUB, Stream CNRM, CROSS, DET, Rnrm Access …µDRAX Input/Output None Access …µDRAWDraw DRAW3DMATRIX Drop DroiteDROP2 Lagrange Dtag DropnDUP DUP2 Dupn Dupdup Egcd EditEditb Egvl EGVElse END ENG EndsubEPSX0 Sign mantissa E sign exponent EQW EqnlibEQ→ Erase Errm ERR0Errn Euler Exlr EvalObj See above →NUM Ex,y = excosy + iexsiny EXP&LNEXP Expan EXP2HYPEXP2POW Expandmod ExpandCOLCT, EXPAND, ISOL, QUAD, Show Result X2+X Expln ExpfitExpm Eyept Fact F0λFactor …µF0λ Modsto FactormodFactors FAST3D Access …µFANNINGFanning Access ! Test LL FC ? C Access …µFAST3D Input/Output NoneFcoef FC? FFT FdistribCF, FC?, FS? FS?C, SF Distrib Access …µFINISH FindalarmFiler Finish Floor FlashevalFONT6 Xunit Nunit Symb FLOORsymb FONT8 FONT7FONT→ →FONT For Free FourierFreeze Xunit Yunit Symb FPsymb FS? FrootsDisplay Area Value Code CLLCD, DISP, Halt CF, FC?, FC?C, FS?C, SF FS?CFunction Exlr Access …µFUNCTIONFxnd Gauss GammaGbasis AXQ, QXA Gcdmod GCDGET GCDMOD, EGCD, IEGCD, LCM GETI, PUT, Puti GetiObjget Grad GORGET, PUT, Puti #n #m Grob1 Graph GramschmidtGreduce DEG, RAD Access …µ→GROB Access …µGRIDMAP Input/Output NoneGridmap →GROB Grobadd GrobGxor →LCD, LCD→ Halftan HadamardHalt GOR, REPL, SUB HEADER→ Head→HEADER Help Hess HermiteHEX CURL, DIV Histogram Hilbert Histplot Access …µHISTPLOT Input/Output NoneHMS HMS+ →HMS HMS→… & 9L HMS + … &9L HMS → Iabcuv HomeHorner Ibernoulli IbasisIBP ABCUV, Iegcd IDN IchinremResults See also Chinrem Iegcd IDIV2DIV2, Iquot Ax+by=c ELSE, END, IFERR, then IferrCase Ifft ∑ Y k e Ifte IFTIlap Obj It depends LAP, Lapl Image…ßIM Rarray Carray Symb IMsymb Indep IncrInform Global Global xstart xend Title Format Resets Init → vals ResetsInput Init PROMPT, STR→ Stack prompt Commandline prompt ResultINT Intvx IntegerINV INTVX, Risch Iquot Command INVMOD2 ResultInvmod Isol IremainderIsom Symb1 Global Symb2 Jordan ISPRIME?Mkisom NEXTPRIME, Prevprime Kerrm KERKEY BASIS, Image →KEYTIME Access …µKEYEVAL Input/OutputKeyeval Kget KEYTIME→Kill Label Lagrange Access …µ→LANGUAGE Input/OutputLANGUAGE→ →LANGUAGE Lapl LAPLast Objn Obj1 LCD→ Lastarg→LCD LCM Ldec Lcxm Libeval LgcdLibs HERMITE, Tchebycheff Limit LimLIN Title, nlib, nport, ...,title, nlib, nport Σline LineLinfit Model Form of Expression Linsolve LininLIST→ →LIST Σlist ListΠlist Access …¹ ¹is the rightshift of the Qkey LNP1 LnameLncollect LOG LocalLn x + Symb LNP1symb Logfit Access !Ø Input/Output Full Command and Function Reference 3139 Access …µLR Input/OutputLSQ Intercept x Slope x MAD LvarDET, INV Lname Main Access …µMAP Input/OutputMant MAP Access …µ↑MATCH Access …µ↓MATCH Input/Output↑MATCH Symb Symb symb Matr MathsMAX Symb Symb , symb Maxσ MaxrMcalc Input/Output See also MEM MeanMenu BINS, MAXΣ, MINΣ, SDEV, TOT, VAR RCLMENU, Tmenu Menuxy MIN MergeMinehunt MENU, Tmenu →MINIFONT MINIFONT→Minit Minr Mitm MinσMkisom 00000000000E-499 Modsto MODModular Mod y Mroot MolwtMsgbox Name Or xunit String Msolvr Mslv Muser Multmod→NDISP EQNLIB, MCALC, MINIT, MITM, MROOT, MSLV, Muser Ndist Access …ß NEG ßis the rightshift of the 1keyNdupn NEG Nextprime NewobNext NIP Access ! Test L not Is the leftshift of the NkeyNot Noval →NUM NsubNUM …µNΣ OBJ→ NumxNumy OFF OCTOldprt … &NL OBJ → Openio Access …µOLDPRTAccess …µOPENIO Over OrderMemory Directory Lorder is the leftshift of the Nkey Global1 ... globaln PA2B2 P2CParametric Xmin, ymin, xmax, ymax, indep, res, axes, ptype, depend Parity Access …µPARITY Input/Output Partfrac Parsurface Pcar PathPcoef Home directoryname 1 ... directoryname n Pcov Access …µPCONTOUR Input/Output NonePcontour Perinfo PdimPerm Xmax, ymax Peval PertblPgdir Pick Pict Pict Command Puts the name Pict on the stackPicture Pinit PIX? Access …µPKTPixoff Pixon Plotadd PlotPmax Pmin Polar PminiFinds the minimal polynomial of a matrix An nxn matrix a Polynomial Access …µPOLARPOP Form of Current Plotting Action Equation POS Input An expression raised to a powerPotential Powexpand PR1 Powmod Predx Predv…µPR1 Object Preval Predy Prlcd PrevprimePrompt Promptsto Propfrac ProotGlobal→ Prompt STO Prstc PrstPrvar Name Name1 name2 Nport global PSI PsdevPsi MEAN, PCOV, PVAR, SDEV, TOT, VAR Ptprop PtaylPurge Symb String or x or xunit or name PUT PushGlobal Global1 ... globaln CLEAR, CLVAR, NEWOB, Pgdir Puti This command sequenceObj put List Obj put List Name MEAN, PCOV, PSDEV, SDEV, VAR PvarPvars Nport namebackup Memory Access …µPVARS Input/OutputPview Pwrfit + c/d*i PX→C→Qπ ̟ + c/ d* ̟ Quad+ c/ d LQ, LSQ Quote QuotArithmetic, !ÞPOLYNOMIAL !« Quotient of the Euclidean division RAD QXARand Rank Ranm Access …µRATIORatio LQ, LSQ, QR RCI RceqRcij Steq RCL Rclalarm Rclf FINDALARM, StoalarmRclkeys Rclmenu Rclσ RclvxRcws RDM …ßL RE RDZCOMB, PERM, Rand Rect RecnRecv REsymb Rename RemainderQuot New name Old name Repeat ReorderRepl END, While RES Plot Type Default IntervalString target String String result Backup To restore a RestoreResultant Slopefield Risch RevlistRewrite Rkferr RKF Is the rightshift 3key Problem for a differential equationRkfstep RND RLBRLB, RR, RRB RNDsymb Roll RnrmRolld Romupload ROT RootROW 3207 →ROW ROW+ROW→ RPL Access … ÃL Byte RRB Is the rightshift of the 3keyRRB RL, RLB, RRB Rref Rref RRK Rrefmod Rrkstep − 2 t + t 2 RKF, RKFERR, RKFSTEP, RRK, Rsberr RsberrRSD Rswp Access … Ã R → BRules DET, IDN →R, IM, RE Same180/̟x →Dsymb Sbrk Access …µSCALEH Input/OutputScale Scaleh AUTO, SCALEH, Xrng ScatrplotScatter Schur Access …µSCATTER Input/Output NoneSCI Sclσ Scroll SconjSdev Send DOSUBS, Stream SEQSeries Seval Server Sidens ShowSigma X1/cm3 Access !ÖDERIV LL Access !ÖDERIV LSigmavx Sign SIMP2 SigntabSIGNsymb ABS, MANT, Xpon SIN SimplifySincos Sin z Sinv SinhSize Sinh z Slopefield SLBString Integer List Vector Symb Grob NEG, SCONJ, Sinv SnegSnrm Solveqn Solve Sort SolverSolvevx Srad SphereSquare Analytic Function Returns the square of the argument SQsymb Srecv SRBCOND, SNRM, Trace ASR, SL, SLB, SR Srepl Access …µSRECVSST SST↓ Step StartSTD Step Access …µSTIMESteq Stime Access Input/Output StoalarmSTO Buflen Stof Access …µSTOFStokeys Óis the rightshift of the 9 key STO+ StoreStovx STO/, + STR→ Stoσ→STR DTAG, EQ→, LIST→, OBJ→, →STR Strm StreamSturm List Obj Result Stws SturmabSUB Sturmab Subtmod SubstX1, y1 X2, y2 CHR, GOR, GXOR, NUM, POS, REPL, Size SVL SVDSwap DIAG→, MIN, SVL SYST2MAT SysevalSylvester 100 y TabvalX, symb Symb 1, symb →TAG TabvarTail →ARRY TAN2CS2 TANTAN2SC Tan z Tanh TAN2SC2Tanh z TANHsymb Taylr TAYLOR0Tchebycheff HERMITE, Legendre Tdelta TcollectTests TDELTAsymb1, symb2 Texpand TevalText Then Time Ticks→TIME Tinc Tline TlinTINCsymb1, symb2 SIMPLIFY, TCOLLECT, Texpand TOT TmenuTrace Tran Trig TransioEffect BAUD, CKSM, Parity Trigo TrigcosTrigsin Trigtan CONJ, Tran TRNTrnc Truth TruncTRNCz TRNCsymb Tstr Access …µTRUTH Input/Output NoneTsimp TVM TvarsTvmbeg Tvmend Type Builtin CommandsUbase Object Type Number User objects UFL1→MINIF UfactUnassign Unassume Unpick Unbind→UNIT Until UnrotUpdir Utpc Utpn UtpfUTPF, UTPN, Utpt UTPC, UTPN, Utpt UVALsymb UtptUval Coordinate System -16, Complex Mode Flag -16 clear Rectangular mode Flag -16 set Polar mode € yX1, x2 X1, x2, ..., xn Xn-2 VAR Vandermonde Vars Access …µVERSION Input/OutputVER Version Variable name Contents opened in the most suitable Editor Variable name Contents opened in the command line EditorVisit Visitb Wait Access ! L in Wait Is the leftshift of the NkeyVtype While WireframeWhile testclause Repeat loopclause END While Repeat Wslog Access …µΣX Input/Output Access …µWSLOGΣX2 Log4 ... log1 Xcol ΣX2Xget Xmit XOR Access …µXMITXnum Xput XponXPONsymb MANT, Sign Command XQ.3658 Results √19/142 Command XQ.3658 Results 1829/5000Xrecv Xrng Xsend Access …µXSENDXserv Input/Output RPN Xxrng XvolΣXY ΣX*Y ΣY2 ΣY2Ycol …µΣY AUTO, PDIM, PMAX, PMIN, Xrng YrngYslice Yyrng YvolZeros EYEPT, XVOL, XXRNG, YYRNG, Zvol Access Q PowerZfactor Zvol √ Square Root WhereZsymb Symbz SQ, , Isol Integrate Access …Á Áis the rightshift of the Ukey? Undefined Lower limit, upper limit, integrand, name Summation ∞ InfinitySigma Plus Results -π/2 Access …µΣ Input/Output Access …µΣ+ Input/OutputSigma Minus X 2, …, x m 1, …, x 1 m x n 1, … , x n m Factorial ∂ Derivative14159265359… Symb Name Xunit Unit attachment PercentXy/100 Symb,x Type Object Description « » Program delimitersLess than #n1 #n2 ≤ Less than or Equal ≥ Greater than or Equal Greater than ≠ Not equal ≠ symb Multiply + Add Subtract Divide Y1/unit = Equal == Logical Equality → Create Local StoreDEFINE, RCL, →, STO … É CLEAR, DROP, DROPN, DROP2 Semicolon Selecting CAS Settings CAS SettingsPoints to note when choosing settings CAS directory, Casdir Computer Algebra System Examples and Help Using the CASCompatibility with Other Calculators Extending the CAS Arithmetic commands Computer algebra command categories listed by menuAlgebra commands, …× Arithmetic Integer commands, !ÞINTEGER Other Arithmetic commands, !Þ Arithmetic Modulo commands, !Þ ModuloArithmetic Permutation commands, !Þ Permutation Calculus commands Matrixrelated commands Exp and Lin commands, !ÐCreate, !Ø Create Operations, !Ø Operations Linear Systems, !Ø Linear Systems Quadratic form, !Ø Quadratic FormLinear Applications, !Ø Linear Appl Eigenvectors, !Ø Eigenvectors Trigonometry commands Symbolic solve commands, !ÎOther Trigonometry commands, …Ñ Hyperbolic, …Ñ Hyperbolic Unit conversion tools, !Ú Units Tools Convert commands, !ÚBase conversion tools, !Ú Base Trigonometric conversions, !Ú Trig Conv Matrix convert, !Ú Matrix Convert Other CAS operations, …µ CAS utility operations CAS menu commands, …µThese commands display menus or lists of CAS operations Equation Reference Equation Reference FLUIDS, 24 *********************3 Variable Description Columns and BeamsΣcr Critical stress Σmax Maximum stress Internal bending moment at Eccentric Columns 1 Elastic Buckling 1Equations Example Equation Simple Deflection 1Simple Slope 1 Simple Shear 1 Solution V=624.387lbfSimple Moment 1 Cantilever Moment 1 Cantilever Deflection 1Cantilever Slope 1 Cantilever Shear 1 Solution V=200lbf Equation Reference Relative permeability ElectricityRelative permittivity Coulomb’s Law 2 Ohm’s Law and Power 2 Solution V1=80V Wire Resistance 2Solution I1=5.6250A Voltage Divider 2 Series and Parallel C 2 Solution R=0.175Series and Parallel R 2 Series and Parallel L 2 Solution V=50VCapacitive Energy 2 Inductive Energy 2 Solution q=0.0020C Equation Reference RLC Current Delay 2DC Capacitor Current 2 Capacitor Charge 2 DC Inductor Voltage 2 Solution V=3.2968VRC Transient 2 RL Transient 2 Resonant Frequency 2 Solution I=0.0072APlate Capacitor 2 Cylindrical Capacitor 2,19 Toroid Inductance 2 Solenoid Inductance 2 Sinusoidal Current 2 FluidsSinusoidal Voltage 2 Bernoulli Equation 3 Pressure at Depth 3Reynolds number Initial and final velocities Flow with Losses 3 Flow in Full Pipes 3 Forces and Energy Linear Mechanics 4 Hooke’s Law 4 Angular Mechanics 4Centripetal Force 4 Drag Force 4 1D Elastic Collisions 4Law of Gravitation 4 MassEnergy Relation 4 Ideal Gas Law 5 Gases Ideal Gas State Change 5 Solution Vf=21Isothermal Expansion 5 Polytropic Processes 5 Real Gas State Change 5 Real Gas Law 5 Kinetic Theory 5 Heat Transfer Conduction 6 Heat Capacity 6Thermal Expansion 6 Conduction + Convection 6 Convection 6 Black Body Radiation 6 MagnetismFba Ia, Ib Force between Wires 7 Straight Wire 7 Magnetic B Field in Toroid 7 Solution B=0.0785TMagnetic B Field in Solenoid 7 Motion Projectile Motion 8 Linear Motion 8Object in Free Fall 8 Circular Motion 8 Angular Motion 8Terminal Velocity 8 Escape Velocity 8 Law of Refraction 9 Optics Brewster’s Law 9 Critical Angle 9 Spherical Reflection 9 Solution n2=1.5000Spherical Refraction 9 Thin Lens 9 Oscillations Example Given L=15cm MassSpring System 10Simple Pendulum 10 Simple Harmonic 10 Conical Pendulum 10Torsional Pendulum 10 Plane Geometry Equations Example Circle 11Ellipse 11 Regular Polygon 11 Rectangle 11 Triangle 11 Circular Ring 11 Cone 12 Solid Geometry Parallelepiped 12 Cylinder 12 Sphere 12 Solid State Devices Drawn mask length PN Step Junctions, or Saturation current densityDrawn gate length Nmos Transistors, or Channel length JFETs PN Step Junctions 13 VDS Nmos Transistors 13 JFETs 13 Bipolar Transistors 13 Xdmax = ⋅ Vbi VGS + VDS Minimum principal normal stress Stress AnalysisMaximum principal normal stress Stress on an Element 14 Normal Stress 14Shear Stress 14 Example Mohr’s Circle 14 Longitudinal Waves 15 WavesTransverse Waves 15,1 Sound Waves 15 References Page Development Library Obj String Development Library Command ReferenceObj1 … objn Symb Obj1, ...,objn Development Library String Obj Debug string Error list BetaTestingString Obj Code String Library n String Error list Edited stringLibrary Object String Ey,z.Et LC~C Obj … obj Obj 1, ...,obj n →LST Obj 1 … obj n Obj 1, ...,obj n Pokearm String1 String2 →S2Returns String Global Xlib Crlib Create Library Command Extension program Introduction Masd The Machine Language and System RPL CompilerStarting Masd Modes Error messages Message Description ErrorsFormat of the error list Labels Links Constants Extable Expressions Macros and includes Operator Priority Directive Description Filename conventionsCompilation directive Docstr !DBGINF directive Bit registers Saturn ASM modeCPU architecture Skips Other notesNew instructions These instructions Are equivalent to Skips instructions Equivalents Tests Syntax Example Saturn instructions syntax Syntax Example DReg=hh See above. This is only valid in emulated Saturn Places the value of Exp in the code, on x nibbles CARRY0 003AA Autousertest ARM architecture ARM mode Description Form Instruction set Operation Assembler Action Flags Offset Element Armsat instructionREG a REG B REG C REG D REG R0 REG R1 REG R2 REG R3 REG R4 Instructions System RPL modeReals and system binary Unnamed local variables Token Description DefinesTokens Code LC 001 Gosbvl Outcinrtn ?CBIT=1.6 Turnmenuoff LC 80100 Armsat Level Disassemblers Library Entry Point Library ExtableNop String String 1, ...,string n Messages Listed Alphabetically Error and Status Messages A1Message Meaning # hex C0C A2 Error and Status Messages Error and Status Messages A3 Σdat A4 Error and Status Messages Error and Status Messages A5 A6 Error and Status Messages C0E Error and Status Messages A7C0B C0D A8 Error and Status Messages # hex Message General Messages Error and Status Messages A9 # hex Message A10 Error and Status Messages OutofMemory Prompts Error and Status Messages A11 A12 Error and Status Messages Stack Errors and MessagesObject Editing Messages Equation Writer Application Messages Error and Status Messages A13 # hex Message FloatingPoint ErrorsArray Messages Statistics Messages A14 Error and Status Messages Mode and Plot Input Form Prompts # hex Message 70F Error and Status Messages A15 73F A16 Error and Status Messages 75F Error and Status Messages A17 78F A18 Error and Status Messages Error and Status Messages A19 Advanced Statistics Messages A20 Error and Status Messages 80F Error and Status Messages A21 82F A22 Error and Status Messages 85F Error and Status Messages A23 87F A24 Error and Status Messages HP Solve Application Messages Error and Status Messages A25Statistics Help Messages Printing # hex Message Unit ManagementTime Messages Programmer’s Doerr Error and Status Messages A27 System Flags Choose Box Prompts A28 Error and Status Messages Error and Status Messages A29 A30 Error and Status Messages Error and Status Messages A31 Prompts A32 Error and Status Messages Error and Status Messages A33 A34 Error and Status Messages Statistics Prompts Error and Status Messages A35 A36 Error and Status Messages Time and Alarm Prompts Error and Status Messages A37 A38 Error and Status Messages Symbolic Application Prompts Plot Application Prompts Error and Status Messages A39 A40 Error and Status Messages Error and Status Messages A41 Solve Application Prompts A42 Error and Status Messages Error and Status Messages A43 A44 Error and Status Messages CAS Messages Error and Status Messages A45 A46 Error and Status Messages Error and Status Messages A47 Filer Application Messages A48 Error and Status MessagesDF0A DF0B DF0C DF0D DF0E DF0F DF1A DF1B DF1C DF1D DF1E DF1F Constants Library Messages Error and Status Messages A49 Equation Library Messages A50 Error and Status MessagesMinehunt Game Prompts MultipleEquation Solver Messages Periodic Table Messages Error and Status Messages A51Financial Solver Messages Development Library and Miscellaneous Messages A52 Error and Status Messages Tables of Units and Constants B1 Units B2 Tables of Units and Constants Tables of Units and Constants B3 B4 Tables of Units and Constants Constant Full Name Value in SI Units Tables of Units and Constants B5 B6 Tables of Units and Constants Properties of Elements Flag Description System FlagsNot used System Flags C1 C2 System Flags System Flags C3 C4 System Flags System Flags C5 C6 System Flags System Flags C7 C8 System Flags Internal use only /0 occurred System Flags C9 User FlagsPage Reserved Variables D1 Contents of the System Reserved Variables Reserved Variables D3 ΒENTER D4 Reserved Variables Exited Reserved Variables D5 Mpar MHparN1, n2 Nmines Reserved Variables D7 BAR, etc D8 Reserved Variables Prtpar Reserved Variables D9 S1, s2 To use for input into the table Parameter Description Default Value CommandNUMX, Numy D10 Reserved Variables Reserved Variables D11 Var1 var2 … varmStatistical Matrix for Variables 1 to m D12 Reserved Variables EXPFIT, PWRFIT, or Logfit Casdir Reserved Variables D14 Reserved Variables Modulo Technical Reference E1 Object SizeObject Type Size bytes E2 Technical Reference Symbolic IntegrationPattern Antiderivative Technical Reference E3 E4 Technical Reference →DEF Expansions Technical Reference E5 Order Operation E6 Technical Reference International Standard publication No. ISO 31/l197 8 E Group 2 Commands that must use Dolist to parallel process Group 1 Commands that cannot parallel processGeneral rules for parallel processing Parallel Processing with Lists F1 Group 6 Oneargument, oneresult commands Group 5 Commands that set modes / statesGroup 4 ADD and + F2 Parallel Processing with Lists Group 8 Multipleargument, oneresult commands Group 7 Two argument, one result commandsGroup 9 Multipleresult commands Group 10 Quirky commands F4 Parallel Processing with Lists Using Dolist for Parallel Processing $ & D $ & C$ & F $ & + ¥ ! &I Keycode Keystroke Definition@ & ³ @ & O ~@ & O Keyboard Shortcuts G3 ~@ & Í @ &†@%VARNAME% = varname G4 Keyboard Shortcuts MenuNumber Table H1 Menu NumbersSyntax Example H2 The MenuNumber Table Menus 0 through MenuNumber Table H3 H4 The MenuNumber Table Menus 118 through MenuNumber Table H5 Menus 178 throughBuiltIn Library Menus Page + key Command MenuPath TableKey ALPHARS2 MTH NXT Prob I2 The Command MenuPath Table Command Type Library Size Keys Menu First Arith Modul MTH List«MODULAR» Addtoreal CAT Algb I4 The Command MenuPath Table PRG Test NXT NXT PRG NXT Modes Flag Chinrem LS&MODE FlagPRG NXT CHR I6 The Command MenuPath Table PRG NXT NXT Time Alrm Delay CAT DelalarmRS&TIME NXT PRG NXT NXT Time NXT I8 The Command MenuPath Table «POLYNOMIAL» EGV PRG NXT NXT Error IferrMTH Matrx NXT Else I10 The Command MenuPath Table I11 I12 The Command MenuPath Table «INTEGER» Calc Deriv NXTPRG Brch NXT «DIFF» NXT NXT I14 The Command MenuPath Table I15 I16 The Command MenuPath Table I17 I18 The Command MenuPath Table I19 I20 The Command MenuPath Table I21 I22 The Command MenuPath Table I23 I24 The Command MenuPath Table I25 I26 The Command MenuPath Table I27 I28 The Command MenuPath Table DUP Menuxy Version Matrices Creat NXT NXT MTH Matrx Make NXT NXTCAT Vtype XLIB~ SLV NXT I30 The Command MenuPath TableAlphalse MTH NXT Const «CONSTANTS» Σlist ΣlinePRG Test «TESTS» NXT →ALG I32 The Command MenuPath Table Ascii Character Codes and Translations J1 Code DescriptionCharacter Codes J2 Ascii Character Codes and Translations Code Trans. Description Index Alpha keyboard Calculator 59, 531 375 Preserving calculator status Flags 132 Last argument Memory Nested structures 545 Programs Range 3115 Serial communications 237, D3 Tagged objects UPs

Gases (5)

Variable

Description

Molecular weight

Pi, Pf

Initial and final pressures

Ideal Gas Law (5, 1)

Equations:

Equation Reference 525