**WEBBOT
NAMES, STATION AND PERIOD**

**Newton's Law of Cooling**

**I. DATA COLLECTION**

1. Open PSLexcelerator and SELECT the
TEMPERATURE probe icon and CALIBRATE by typing in the **number
taped** to your temperature probe for PROBE A and by choosing **extended**.
Say YES to placing it in the column to the right of $C:$C. Next,
Click on the EXPERIMENT CLOCK in column C and tell the probe to
collect **3 samples** per second for **5 minutes**
producing a total of **900 samples**. Next go over to **PSL**
on the menu and click on **PREVIEW MEASUREMENTS** to make sure
that your PSL interface is working. When the temperature
stabilizes, note and record this initial temperature as your
original ROOM TEMPERATURE value for use in your spreadsheet
later. ________________

2. After the ROOM TEMPERATURE appears to be
stable, get a sample of hot water and place the probe into the
water. While still in PREVIEW, watch the probe's temperature
increase until it seems to stabilize at a temperature in the
range between 80 -100^{o}C. When this occurs, leave the
probe in the water, STOP PREVIEW, go over to **PSL** on the
menu and click on **FAST DISPLAY, CREATE** **FAST GRAPH.**
After the graph appears on your screen, click on the **green
"G" icon** to start recording your measurements. The
PSL will begin to record the probe's temperature data on your
graph. After about 3 -5 seconds, take the probe from the hot
water and hold it VERY STILL in a "draft free" location
until it cools back down to room temperature OR until the time
runs out.

3. When the computer is finished taking
data, move to **FILE, SAVE AS**, and save your file with the
following filename format: **period_station_temp.** Record
your filename here ________________

[For example, a student in 3rd period at lab station #6 would save his file as

period3station6temp[NOTE that you should NOT add a file extension -- PSL automatically adds a.xlsextension while saving.]

The PSL program will then let you input a description. Be sure to include your names and the date in the description. Don't forget to unplug the PSL adapter from the AC outlet at your table.

4. After you have saved your file, **EXPERIMENT
(CLOCK) TIME** should be in column C and (**PROBE A)
TEMPERATURE **in column D. In cell **E5** type **A-RT**;
in cell **E6** type **C**; in cell **F5** type **LN(A-RT)**;
in cell **G5** type **Room**; and in cell **G6 **enter
just the numerical value (do not include °C) of the **original
room temperature** recorded in step 1 above.

5. You are now going to program the cells
in column E so that the room temperature value in G6 is
subtracted from every value recorded under **Temp A** by the
PSL probe - this will calculate the probe's relative temperature,
that is, how much higher the probe's temperature was above room
temperature.

First go to cell E7 and type **=D7-$G$6**
and press ENTER. To highlight column C, keep your cursor in E7,
press SHIFT (keep it engaged) and use the DOWN ARROW to highlight
as much of column E until you reach the last row where column D
has an entry. Then release the SHIFT key, and press **ALT E**dit**,**
F**i**ll Do**w**n.** This will copy your formula
throughout column E. **When this has been successfully
accomplished, update your file by clicking **F**ile **S**ave.
You can also drag your mouse down column E, but be careful to
start in E7 and to not overshoot your last entry (somewhere
around E907).

6.** **Now go to cell F7, type in the
formula **=LN(E7)** and press ENTER. Format this cell entry by
going to **FORMAT, CELLS, NUMBER**, **3** decimal places.
This formula also needs to be filled down throughout all of
column F. Do this by first placing the cursor on F7, and then
pressing SHIFT and the DOWN ARROW simultaneously. When you reach
the last row where column D has an entry, release the SHIFT key,
and press **ALT E**dit, F**i**ll do**w**n. This will
copy your formula throughout column F. You can also drag your
mouse down column F, but be careful to start in F7 and to not
overshoot your last entry (somewhere around F907).

7. While at the bottom of column F, look over the last entries in both columns E and F. Since the natural logarithm function is only defined on domain values for x > 0, make sure no entries in column E are 0 or negative; if they are, they should be accompanied by ERROR or #NUM statements in column F. Those data points must be deleted from your columns before you create your next graph in step 9. You can remove them by placing your cursor in each BAD cell and pressing the grey DELETE key.

8. Resave your file. [**F**ile **S**ave]

9. We are now going to create and EXCEL
graph (called a CHART) from the data recorded in columns C and F.
Begin by placing your cursor in C7, hold down the SHIFT key and
DOWN ARROW simultaneously until you have highlighted all entries
in column C. Then, CAREFULLY press down the CTRL key and release
the SHIFT key. Do NOT release the CTRL key! Column C should
remain highlighted. While continuing to keep the CTRL key
engaged, use the mouse to move your cursor to F7, press down the
SHIFT key (CRTL is still engaged!) and highlight column F as
well. When both columns are highlighted, release both the SHIFT
and CTRL keys and move over on the menu to **INSERT, CHART**.
Choose **xy-scatter, **type in the **title** as **your lab
station number and group members' last names**, **x-axis**
is **time (sec)** and **y-axis** is **LN (A - RT)**.
Turn off LEGEND. Finally choose **SAVE AS NEW SHEET**. Your
graph (CHART1) should now appear on its own worksheet. Check it
for any mistakes, and if everything is okay, print it by moving
to **ALT F**ile, **P**rint. To correct an error, just click
on that region of the graph and you should get an active window
for editing.

10. Resave your file. [**F**ile **S**ave]

11. Click on your GRAPH, a **+**
should appear on your graph telling you the co-ordinates of any
given data point. Drag the cursor along the graph until you reach
what appears to be the beginning of the **longest, diagonal
"straight line section" of the graph** (do not choose
the flat plateau that initially starts your graph, that region
represents the time when the probe was in the hot water bath.).

Record the time of that initial location here ____________.

13. We must now determine the equation of
the straight line segment's regression line. This is done by
clicking on the graph to get the yellow squares n , then move to **chart **on the menu,
add **trendline**, **linear**, and
under **Options**, choose **display equation **and**
R² values** on chart. When this is complete, print (**ALT
F**ile **P**rint) your graph and resave your file. [**F**ile **S**ave]

14. Mathematically, the half-life
represents the amount of time required for a given quantity to be
cut "in half." Our probe's data for **relative
temperature (A-RT) vs time** displays the behavior of an
exponential decay. It is therefore a reasonable next step to
determine the probe's half-life.

At this time, we will calculate the
half-life of your group's PSL temperature probe by using the
following equation and the slope from your graph of **LN(A-RT)
vs tim****e:**

**form
field**

15. In EXCEL, open your spreadsheet and
fill out the following data table by scrolling down your data
table in column A until you find the time you recorded from step
12. Note the corresponding value for A-RT in column C and record
it in your chart. Then scroll down to the time closest to the
next time calculated in your chart in step 15 and record that
time's corresponding value for A-RT in your chart. Continue this
procedure until all 180 seconds have been examined. Then complete
the column entitled **ideal (A-RT) value.**

**form
field**

**II CONCLUSION**

Did the amount of heat radiated by the probe, as reflected by the changes in its relative temperature [A-RT] in Step 15, behave according to the definition of half-life? Why or Why not? Support your answer by using you data analytically to calculate a percent difference/error for your closest example.

**form field**

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EXTRA CREDIT: __Explain__ **and**
give a __specific procedure__ for each of the following
spreadsheeting terms, operations and skills:

**INSERT
A CHART (13 x 2) WITH FORM - blanks to be filled in**

saving a file with a new name _____

saving a file while keeping its current name _____

opening an existing file _____

cell address _____

fixing the number of decimals in a number _____

centering an entry in a cell_____

notation which begins EVERY formula _____

notation to raise a number to a power_____

notation to add up the entries from C1 to C10 _____

notation to take the square root of the number in cell D2 _____

notation to take the natural logarithm of the number in cell D2 _____

coping a formula in a topmost cell throughout a column__________________________________

freezing the cell address A5 in a formula so that it will not change when the formula is copied elsewhere ________