ࡱ> \_  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[^Root Entry F@J7pHk-]WorkbookYSummaryInformation(DocumentSummaryInformation8, \pDan Ba==-[, 8X@"1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Calibri1Calibri1Arial1Arial1h8Cambria1,8Calibri18Calibri18Calibri1Calibri1Calibri1<Calibri1>Calibri1?Calibri14Calibri14Calibri1 Calibri1 Calibri1Calibri1Calibri1 Calibri1Calibri1Calibri1hCalibri1Calibri1Calibri1hCalibri1hCalibri1Calibri1Arial1Arial1Calibri"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)0.0 0.000 #,##0.0 0.000E+00 0.00000                                                                      ff + ) , *     P  P        `            a>       @            $ "8@@ "<@ "8@ "8 @  @@  @   @   (  ( "8@ "0@ "0@ "4 "0 "0  "4 "0 "4  "4 "4 "4  $  "p@ "p "t "t  "t  "8 @ )  *8@  @ "x@ @  $@  d@   $@ "4 "t  "4  (@ ||nޝ}A} 00\);_(*ef;_(@_) }A} 00\);_(*ef;_(@_) }A} 00\);_(*ef;_(@_) }A} 00\);_(*ef;_(@_) }A} 00\);_(*ef;_(@_) }A} 00\);_(*ef ;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L ;_(@_) }A} 00\);_(*23;_(@_) }A} 00\);_(*23;_(@_) }A} 00\);_(*23;_(@_) }A} 00\);_(*23;_(@_) }A}  00\);_(*23;_(@_) }A}! 00\);_(*23 ;_(@_) }A}" 00\);_(*;_(@_) }A}# 00\);_(*;_(@_) }A}$ 00\);_(*;_(@_) }A}% 00\);_(*;_(@_) }A}& 00\);_(*;_(@_) }A}' 00\);_(* ;_(@_) }A}( 00\);_(*;_(@_) }}) }00\);_(*;_(@_)    }}* 00\);_(*;_(@_) ??? ??? ??? ???}-}/ 00\);_(*}A}0 a00\);_(*;_(@_) }A}1 00\);_(*;_(@_) }A}2 00\);_(*?;_(@_) }A}3 00\);_(*23;_(@_) }-}4 00\);_(*}}5 ??v00\);_(*̙;_(@_)    }A}6 }00\);_(*;_(@_) }A}7 e00\);_(*;_(@_) }x}800\);_(*;_(  }}9 ???00\);_(*;_(??? ???  ??? ???}-}; 00\);_(*}U}< 00\);_(*;_( }-}= 00\);_(*}(}]00\);_(*}(}^00\);_(*}(}_00\);_(*}(}`00\);_(*}(}a00\);_(*}(}h00\);_(*}(}k00\);_(* 20% - Accent1M 20% - Accent1 ef % 20% - Accent2M" 20% - Accent2 ef % 20% - Accent3M& 20% - Accent3 ef % 20% - Accent4M* 20% - Accent4 ef % 20% - Accent5M. 20% - Accent5 ef % 20% - Accent6M2 20% - Accent6  ef % 40% - Accent1M 40% - Accent1 L % 40% - Accent2M# 40% - Accent2 L湸 % 40% - Accent3M' 40% - Accent3 L % 40% - Accent4M+ 40% - Accent4 L % 40% - Accent5M/ 40% - Accent5 L % 40% - Accent6M3 40% - Accent6  Lմ % 60% - Accent1M 60% - Accent1 23 % 60% - Accent2M$ 60% - Accent2 23ٗ % 60% - Accent3M( 60% - Accent3 23֚ % 60% - Accent4M, 60% - Accent4 23 % 60% - Accent5M0 60% - Accent5 23 %! 60% - Accent6M4 60% - Accent6  23 % "Accent1AAccent1 O % #Accent2A!Accent2 PM % $Accent3A%Accent3 Y % %Accent4A)Accent4 d % &Accent5A-Accent5 K % 'Accent6A1Accent6  F %(Bad9Bad  %) Calculation Calculation  }% * Check Cell Check Cell  %????????? ???+ Comma,( Comma [0]-&Currency.. Currency [0]/Explanatory TextG5Explanatory Text % 0Good;Good  a%1 Heading 1G Heading 1 I}%O2 Heading 2G Heading 2 I}%?3 Heading 3G Heading 3 I}%234 Heading 49 Heading 4 I}% 5InputuInput ̙ ??v% 6 Linked CellK Linked Cell }% 7NeutralANeutral  e%"Normal 8Noteb Note   9OutputwOutput  ???%????????? ???:$Percent ;Title1Title I}% <TotalMTotal %OO= Warning Text? Warning Text %XTableStyleMedium9PivotStyleLight16`\8 Newtons Lawh\Newtons Law with Logsg/  !3 A@@  9$ Constants:Newton's law of CoolingK Temp. (C) C ln(e-kt)T0 - Ts  T - Ts K (s-1)Average&Predicted temperature at 15 minutes = Relative Error =%Ts T(t) = Ts + (T0 - Ts) e-Kt    Law: Time (mins)CTime (s) Time (min)min-1s-1K =T - Ts T0 - Ts   ln[(T(t) - Ts)/(T0 - Ts)]    $Calculaion of K from Slope of Graph: (using average K value) Transform: ln[(T(t) - Ts)/(T0 - Ts)] = -Kt   Tpredicted (C) Calculation of K Using Averages(2Calculation of K Using Logarithmic Transformation:(Relative Error Average Error'Predicted temperature at 30 minutes = * 4 4f5h5J7LccB  !v9II  dMbP?_*+%&ffffff?'ffffff?(?)?"B333333?333333? l&<3U} $}  !h;;;      ? C A ~ @ A AB CB A AB F G H H H IORU@RRSTP?R@@RgffffN@ LDR O@ DD/YA~?DDAUa1S,? LL< P@R@ R33333M@  R O@  Yt w?  #  LLA U|`3? P@R@ RgfffffM@  R O@  Yϳ?   Ulcy3? ~ P@ RfffffS@ RL@  R O@  YVߺ)в?   U)!=4?  P@RS@ RLL@  R O@  Y&?   U:B4?  P@R2@ R33333K@  R O@  Y}E:?   U{"&4? P@RS@R K@R O@Y ? U5? P @R.@RgfffffJ@R O@Y[T ? Ubf&6?~ P"@RYR@RI@R O@Y? UAF6?P$@Rp@R33333sI@R O@Y%u? Uo,5?P&@R @R33333H@R O@Y<+.?#LLAUZ5?LL<P(@RQ@ŘH@R O@YV$?U;BCa5?~ P*@RyQ@RH@R O@Y?y{?UM5?P,@R@Q@ŘG@R O@Y2U»?Us75?P.@R@R333333G@R O@YhX?Uv(85?~ P<@SRRYUP=@SR@!RgffffB@ DD!R O@ DDYC7?UHꮲ2?P>@S@!RB@ DD!R O@ DDYe?U3-B2?Q?@V@M@!WLB@ DD!W O@ DDZAm?Xǘ۠2?JKKKKL @>> M N#ES,\4? %B A 9Q@ A>W08&T("S  A / D2qp|?DDADd A c6    ((  (n ( c 4NChart 100]@`Ӹ  PP PZaajk&hfffff?'hfffff?(?)?"@XX533333?533333?3&<3PH0(  h)3d23   MR R R RI3~S S4 3Q:  Temp. (C)Qr ;Q ;Q3_ M MM f aaa@"B  ` R R R Rï R "'xS S4ES S 4D$% 03O& QR R40S S4$% 3O& Q4FA1 3OFQ 3*N& ! R RR R0u,S S43*I@N & ! R R0u,bS S4% `A 3O D&!Q  Time (mins)23 M NMR RR Re]S S4'< @ xxxxxxxxxxx xS S4% 3s Z3O"c&!Q $Temperature (C)23 M NMR RR Rp]S S4'<7# xxxxxxxxxxxxxxxx xS S4523 M  MR Rn]S S43d" 4S S4DFQ % Se3O+&"Q 2Newton's Law of Cooling23 M NMR RR Rt]S S4'#}. xxxxxxxxxxxxxxxxxxxxxxx xS S4b [S S 4eee  C2  >@bbggD  H`px  dMbP?_*+%&ffffff?'ffffff?(?)?M6HP DeskJet 812CXC od,,LetterDINU"4$%#| $$$$"d,,333333?333333?&<3U} }  }  } } I }  H w;;;      c ? CAA C A ~ @ A AB CB A AB F G H H H I ORU@ RRST P?R@@! RgffffN@  D D! R O@  D D/ YA~? D D A Ua1S,?  LL< P@R@! R33333M@  D D! R O@  D D Yt w?  # LLA U|`3?   P@R@! RgfffffM@  D D! R O@  D D Yϳ?   Ulcy3?  ~ P@ RfffffS@! RL@  D D! R O@  D D YVߺ)в?   U)!=4?  P@RS@!RLL@ DD!R O@ D DY&? U:B4?  P@R2@!R33333K@ DD!R O@ D DY}E:? U{"&4? P@RS@!R K@ DD!R O@ D DY ? U5? P @R.@!RgfffffJ@ DD!R O@ D DY[T ? Ubf&6? ~ P"@RYR@!RI@ DD!R O@ D DY? UAF6? P$@Rp@!R33333sI@ DD!R O@ D DY%u? Uo,5? P&@R @!R33333H@ DD!R O@ D DY<+.? UZ5? P(@RQ@!ŘH@ DD!R O@ D DYV$? U;BCa5? ~ P*@RyQ@!RH@ DD!R O@ D DY?y{? UM5? P,@R@Q@!ŘG@ DD!R O@ D DY2U»? Us75? P.@R@!R333333G@ DD!R O@ D DYhX? Uv(85? ]^__`aP=@SR@!RgffffB@ DD!R O@ D DYC7? UHꮲ2? P>@S@!RB@ DD!R O@ D DYe? U3-B2? Q?@V@M@!WLB@ DD!W O@ D DZAm? Xǘ۠2? JKKKKL @>> M N#ES,\4?6 % B@D8&T( !"$w&;'(;*;,./1;23456789:;<=>? A#~ l@ A !A "A /"D :@GD DADd "A $? &C&B &A 'CBA'A (C(B (A(A *C *A ~ *@ *A ,C .A.A rh? .A/\@Zf2?C D.< /A 1F 1F 1G 1d 1b 1f!~ 2O2P D2<~ 2RU@42Y/D2DD2DAD2jU@A.D*D2D*@D/<D2A@/2e4D2D2AD2d~ 3P?3PN@433E L<~ 3R@@43YA~?4D3DD2DAD3j DT@2.D*D2D*@D/<D3A@/3g滜?3D3D3AD3d~ 4P@4P^@53~ 4R@44Yt w?5D4DD2DAD4jmm8L${T@3.D*D2D*@D/<D4A@4g,j?54#4ELLALd~ 5P@5Pf@63~ 5R@45Yϳ?6D5DD2DAD5jWB[6c:T@4.D*D2D*@D/<D5A@5g}zL?64~ 6P@6Pn@736RfffffS@46YVߺ)в?7D6DD2DAD6j y5S@5.D*D2D*@D/<D6A@6gF 򤠈?74~ 7P@7Pr@83~ 7RS@47Y&?8D7DD2DAD7j1"S@E.D*D2D*@D/<D7A@7grz?84~ 8P@8Pv@93~ 8R2@48Y}E:?9D8DD2DAD8jZ5ę~S@7.D*D2D*@D/<D8A@8ga4Q?94~ 9P@9P@z@:3~ 9RS@49Y ?:D9DD2DAD9j!fsBS@8.D*D2D*@D/<D9A@9gW!|?:4~ :P @:P~@;3~ :R.@4:Y[T ?;D:DD2DAD:j1S@9.D*D2D*@D/<D:A@:gZ7A?;4~ ;P"@;P@<3;RYR@4;Y?<D;DD2DAD;jz蟘&R@:.D*D2D*@D/<D;A@;gSH @<4~ <P$@<P@=3~ <Rp@4<Y%u?=D<DD2DAD<jTR@;.D*D2D*@D/<D<A@<gl7Pd@=4~ =P&@=P@>3~ =R @4=Y<+.?>D=DD2DAD=j,$$ZR@<.D*D2D*@D/<D=A@=gs@>4~ >P(@>P@?3~ >RQ@4>YV$??D>DD2DAD>jR0ڒ"R@=.D*D2D*@D/<D>A@>g#Z@?4~ ?P*@?P`@@3?RyQ@4?Y?y{?@D?DD2DAD?jyYQ@>.D*D2D*@D/<D?A@?gMr@@48h*O&08.1T@ABCDEFG~ @P,@@P@@A3~ @R@Q@4@Y2U»?AD@DD2DAD@j%,;Q@?.D*D2D*@D/<D@A@@g=&WBk@A4~ AP.@AP @C3~ AR@4AYhX?CDADD2DADAj mQ@@.D*D2D*@D/<DAA@Ag"+Pl,@C4B]]^`kh~ CP=@CP0@D3~ CSR@4CYC7?DDCDD2DADCjFeAM@3.D*D2D*@D/<DCA@Cg.s?D4~ DP>@DP @E3~ DS@4DYe?EDDDD2DADDjjTkM@.D*D2D*@D/<DDA@Dgd ?E4~ EQ?@EQ@23~ EV@M@4EZAm?2DEDD2DADEl9dGM@D.D*D2D*@D/<DEA@Ei>V7?34 FJL Gm"#G[(L?2 %2EB;  (4@D(  Dn D c 4NChart 1 -]@w  PP PZaajk&jfffff?'jfffff?(?)?"@XX733333?733333?3&<3PH0(  3,3d23   MR R R RI3~S S4 3Q:  Temp. (C)Qr ; Q ; Q3_ M MM f aaa@"B  ` R R R Rï R "'xS S4ES S 4D$% 03O& QR R40S S4$% 3O& Q4FA|D 3O+  W 3*N& ! R RR R0u,S S43*I@N & ! R R0u,bS S4% b 3O D&!Q  Time (mins)23 M NMR RR Re]S S4'< @ xxxxxxxxxxx xS S4% <} Z3O"c&!Q $Temperature (C)23 M NMR RR Rp]S S4'<7# xxxxxxxxxxxxxxxx xS S4523 M  MR Rn]S S43d" 4S S4D+  W % R 3O+&"Q 2Newton's Law of Cooling23 M NMR RR Rt]S S4'#}. xxxxxxxxxxxxxxxxxxxxxxx xS S4b [S S 4eee    vn D c 4NChart 31 E]@Z  PP PZaajk&ffffff?'ffffff?(?)?"333333?333333?3&<3` *PH0(  ,3d23   MR R R RI3~S S4 3Q:1 6ln[(T(t) - Ts)/(T0 - Ts)]Q ;2EQ ;2EQ3_ M MM  NR R R R28 2  "'S S4ES S 4 3QQQQ3_  MM  MMdR R R R2JS S4JKS S 4D$% 03O& QR R40S S4$% 3O& Q4FA#  3O3F 3* & ! R RR R0u,bS S43*N  & ! R Rbu,bS S4% > 3OD&!Q  Time (mins)23 M NMR RR Re]S S4'<@ xxxxxxxxxxx xS S4% M Z3O,&*P>!#!#! # $!#$!#$!Q 8-ln[(T(t) - Ts)/(T0 - Ts)]23 M NMR RR R[]S S4'<{ΰ xxxxxxxxxxxxxxxxxxxxxxxxxx S S43d" 4S S4D3F % PW 3O4)& P>"%"%" % & "%&"%&""Q H"ln[(T(t) - Ts)/(T0 - Ts)] vs. Time23 M NMR RR R(]S S4' xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xS S4% @ 3OB+& P ' Q23 M NMR RR R]S S4'<%_̿VS?40S S4b [S S 4eee  >*@bb  ggD  Oh+'0@HXd | AdminXPDanMicrosoft Excel@C@4-՜.+,0 PX|  Robert Morris University  Newtons LawNewtons Law with Logs  Worksheets F&Microsoft Office Excel 2003 WorksheetBiff8Excel.Sheet.89qCompObj r