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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 78 "Dr. Sarah'
s Demo on the Cooling Experiment of Cafe Au Lait Versus Black Coffee" 
}{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 
1 {PARA 3 "" 0 "" {TEXT -1 20 "Classroom Experiment" }{TEXT 286 1 " " 
}{TEXT 287 17 "Read this section" }}{EXCHG {PARA 0 "" 0 "" {TEXT 274 
9 "Materials" }{TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 10 "1 CBL Uni
t" }}{PARA 0 "" 0 "" {TEXT -1 31 "2 Calculators with Heat Program" }}
{PARA 0 "" 0 "" {TEXT -1 13 "1 Ceramic Mug" }}{PARA 0 "" 0 "" {TEXT 
-1 23 "4 Refrigerated Creamers" }}{PARA 0 "" 0 "" {TEXT -1 6 "Coffee" 
}}{PARA 0 "" 0 "" {TEXT -1 78 "1 Apparatus to Ensure that Thermometer \+
will Measure from the Center of the Mug" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 275 18 "Experiment Helpe
rs" }{TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 15 "1 Coffee Pourer" }}
{PARA 0 "" 0 "" {TEXT -1 17 "1 Stopwatch Timer" }}{PARA 0 "" 0 "" 
{TEXT -1 50 "1 Person to watch and mark down select data points" }}
{PARA 0 "" 0 "" {TEXT -1 17 "2 Creamer Helpers" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 278 17 "Room Temper
ature:" }}{PARA 0 "" 0 "" {TEXT -1 62 "Dr. Sarah measures room tempera
ture before the class starts (~" }{TEXT 277 12 "24 degrees C" }{TEXT 
-1 1 ")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT 276 45 "Experiment Procedure for Black Coffee Cooling" }
{TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 113 "Dr. Sarah sets up CBL u
nit and Calculators to measure every 4 seconds for 99 readings for a t
otal of 396 seconds." }}{PARA 0 "" 0 "" {TEXT -1 58 "When she says \"g
o\", the following occurs at the same time:" }}{PARA 0 "" 0 "" {TEXT 
-1 48 "The coffee pourer pours the coffee into the mug." }}{PARA 0 "" 
0 "" {TEXT -1 58 "The stopwatch starts counting to 5 minutes and 30 se
conds." }}{PARA 0 "" 0 "" {TEXT -1 35 "The CBL unit starts measuring d
ata." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "T
he temperature watcher records the highest temperature achieved before
 cooling at " }{TEXT 271 12 "72 degrees C" }{TEXT -1 1 "." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 125 "When the stopwatc
h timer beeps at 5 minutes and 30 seconds, the creamer helpers each po
ur a creamer into the coffee, and the " }}{PARA 0 "" 0 "" {TEXT -1 43 
"temperature watcher records the temperature" }}{PARA 0 "" 0 "" {TEXT 
-1 25 "when the timer went off (" }{TEXT 272 14 "63.5 degrees C" }
{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 55 "The temperature watcher records the final temperature (" 
}{TEXT 273 12 "59 degrees C" }{TEXT -1 1 ")" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 280 52 "Experiment Procedure for Cafe Au Lait Co
ffee Cooling" }{TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 113 "Dr. Sara
h sets up CBL unit and Calculators to measure every 4 seconds for 99 r
eadings for a total of 396 seconds." }}{PARA 0 "" 0 "" {TEXT -1 58 "Wh
en she says \"go\", the following occurs at the same time:" }}{PARA 0 
"" 0 "" {TEXT -1 48 "The coffee pourer pours the coffee into the mug.
" }}{PARA 0 "" 0 "" {TEXT -1 44 "The stopwatch starts counting to 30 s
econds." }}{PARA 0 "" 0 "" {TEXT -1 35 "The CBL unit starts measuring \+
data." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 122 
"When the stopwatch timer beeps at 30 seconds, the creamer helpers eac
h pour a creamer into the coffee and the temperature " }}{PARA 0 "" 0 
"" {TEXT -1 42 "watcher records the coffee temperature at " }{TEXT 
281 15 "73.5 degrees C." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 55 "The temperature watcher records the final temperatur
e (" }{TEXT 279 14 "61.5 degrees C" }{TEXT -1 1 ")" }}}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 19 "Classroom Anal
ysis " }{TEXT 288 0 "" }{TEXT 289 30 "Execute the Following Commands" 
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Let's Look at Newton's Law of Co
oling:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "CoolingDerivative:=unapply(k
*(M-T),T);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 293 52 "What is k, M and T
 (Describe in words, not numbers)?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "M:=24;" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT 292 29 "Explain how we obtained M=24?" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 144 "Let's solve the d.e. w
ith out initial condition of T(0)=72 (the highest temperature achieved
 before the coffee started dropping is approximately" }}{PARA 0 "" 0 "
" {TEXT -1 40 "the initial temperature of the coffee). " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "NewtonsLawofCooling:=unapply(rhs(ds
olve(\{diff(T(t),t)=k*(M-T(t)),T(0)=72\},T(t))),t);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 40 "k:=solve(NewtonsLawofCooling(330)=63,k);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 314 29 "Where did I obtain T(330)=63
?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 312 116 
"Execute a Maple Command to find the rate of change of cooling (as a d
ecimal) for Black Coffee at  approximately T=72" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 313 118 "Exec
ute a Maple Command to find the rate of change of cooling (as a decima
l)  for Cafe Au Lait at approximately T=68.5" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 310 106 "Which \+
cools faster (ie which has a greater magnitude of rate of change of co
oling)?  Explain why in words " }}{PARA 0 "" 0 "" {TEXT 311 78 "using \+
your above calculations, and also using the Newtons' Law of Cooling d.
e." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 92 "NewtonsLawofCoolingAuLait:=unapply(rhs(dsolve(\{diff(T(t),t)=k*(
M-T(t)),T(0)=68.5\},T(t))),t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 36 "CBL Unit Temperature Data and Plots " }
{TEXT 290 0 "" }{TEXT 291 30 "Execute the Following Commands" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "times:= [4*i$i=8..396/4]:" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 692 "black_data := # [46.06, 5
7.06, 63.42, 67.29, 69.47, 70.71, 71.56,\n[72, 72, 72, 71.78, 71.56, 7
1.35, 71.13, 70.86, 70.65, 70.44, 70.17, 70.23, 70.02, 69.81, 69.61, 6
9.41, 69.2, 69.2, 69, 69, 68.8, 68.54, 68.40, 68.34, 68.14, 68.14, 67.
94, 67.74, 67.74, 67.55, 67.36, 67.36, 67.16, 67.16, 66.97, 66.97, 66.
78, 66.78, 66.59, 66.59, 66.39, 66.39, 66.21, 66.02, 66.02, 65.96, 65.
83, 65.77, 65.58, 65.58, 65.40, 65.40, 65.33, 65.15, 65.15, 65.15, 64.
96, 64.96, 64.78, 64.78, 64.78, 64.69, 64.54, 64.42, 64.42, 64.17, 64.
17, 63.99, 63.99, 63.81, 63.81, 63.63, 63.63, 63.46, 63.46, 63.28, 62.
93, 61.72, 60.88, 60.38, 59.89, 59.56, 59.56, 59.4, 59.33, 59.33, 59.2
4, 59.24, 59.17, 59.17, 59.01, 59.01]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 698 "aulait_data :=
 # [45.6, 58.66, 65.33, 68.81, 70.88, 72.19, 73.08,\n[ 73.47, 73.24, 7
1.04, 69.77, 68.75, 68.35, 67.95, 67.75, 67.75, 67.49, 67.49, 67.3, 67
.3, 67.3, 67.1, 67.1, 67.1, 67.1, 66.91, 66.91, 66.91, 66.91, 66.91, 6
6.65, 66.72, 66.65, 66.46, 66.46, 66.46, 66.46, 66.27, 66.27, 66.27, 6
6.08, 66.08, 66.08, 66.08, 65.89, 65.89, 65.58, 65.7, 65.52, 65.52, 65
.52, 65.27, 65.33, 65.27, 65.27, 65.08, 65.08, 64.89, 64.71, 64.71, 64
.53, 64.35, 64.16, 63.98, 63.98, 63.8, 63.44, 63.44, 63.27, 63.27, 63.
2, 63.2, 63.27, 63.27, 63.03, 62.85, 62.67, 62.67, 62.67, 62.5, 62.5, \+
62.5, 62.32, 62.32, 62.15, 62.15, 61.98, 61.98, 61.98, 61.98, 61.98, 6
1.98, 61.98, 61.98, 61.98, 61.98, 61.81, 61.63, 61.63]:" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 40 "pts := (x,y) -> zip((x,y)->[x,y], x, y):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "plot([pts(times, black_data), pts(
times, aulait_data)], style=point, symbol=diamond, color=[black,brown]
);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 344 81 "From the graph, how can yo
u tell which has a greater rate of change of cooling?  " }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 345 62 "From the graph, how can you tell which takes less
 time to cool" }{TEXT -1 1 "?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 
58 "Comparison of CBL Unit Plots and Classroom Analysis Plots " }
{TEXT 346 30 "Execute the Following Commands" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "newtonaulait:=plot
(NewtonsLawofCoolingAuLait(t),t=0..1000):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 52 "newtonblack:=plot(NewtonsLawofCooling(t),t=0..1000)
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "dataplot:=plot([pts(t
imes, black_data), pts(times, aulait_data)], style=point, symbol=diamo
nd, color=[black,brown]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
43 "display(dataplot,newtonblack,newtonaulait);" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT 343 140 " Why does the black coffee stop following Newton's
 Law of Cooling arount time 300?  Why doesn't cafe au lait follow Newt
on's Law of Cooling?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 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 "" }}}}{MARK "0 0 1" 11 }
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