SCH 4UM
Charles Law Lab
Jeff Cui, Isaac Chandra, Eli Deng
Qualitative Observations:
General Observations:



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The capillary tube used was constant throughout the whole experiment however the meniscus
appeared to be slanted at times
The beaker used to heat water was not consistent
At times the capillary tube came very close to being submerged in water however never fully
No two trials in the same iteration were done sequentially rather, trials in different iterations were
done before completing the rest of the trials of the original iteration
The ruler-capillary tube apparatus often was used as the stirring tool of the water
The water was only stirred after heating not during the heating
Iteration 1:
Trial 1

Much of the volume of the cylinder comprised of ice cubes and therefore several were to be
removed as the temperature was deemed to be too cold
Trial 2
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Temperature increased beyond the acceptable amount of 5 Celsius and therefore more ice cubes
were added
Trial 3
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A different cylinder of ice water was used because another group impatiently had taken the one
used in the previous two trials
Iteration 2:
Trial 1
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Aggressive mixing of the water in the beaker made the ruler-tube apparatus spin around until lab
partner demanded perpetrator to take apparatus out before mixing
Trial 2
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The heating device was noticeably more aged
Nothing unusual with apparatus
Trial 3
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Superfluous tape component meant to differentiate from other rulers falls off
Nothing unusual becomes of this loss
Iteration 3
Trial 1
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Mr. Cook
SCH 4UM


Charles Law Lab
Jeff Cui, Isaac Chandra, Eli Deng
The size of the beaker shrinks in an attempt to lower heating times as less volume is needed to
submerge the capillary tube
Nothing unusual comes with this change
Trial 2
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Beaker water is overheated due to lack of supervision and is let to cool
Reading appears to not be impacted
Trial 3
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Before testing begins, lab partner demonstrates fragility of thermometer by breaking it in a beaker
by knocking it back and forth of the walls of the beaker
This measurement is taken with a different thermometer
Iteration 4:
Trial 1
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When measuring the length of it was noticed that the trapped gas rapidly changed after removing
from the heated water
Trial 2
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Similar to previous trial trapped gas length decreased rapidly
In this trial only the person performing the measurements changes due to a needed bathroom
break
Trial 3
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Temperature was too hot and was left to rest back down to the designated temperature before
measurements were taken
Iteration 5:
Trial 1
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Shoddy tape quickly washed off following closely to a retaping of the gas tube back onto the ruler
The measurement was only done after the retaping
Trial 2
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Nothing notable occurs during this trial
Trial 3
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Instead of following procedure of using designated tongs to remove the now hot beaker, a hand
was used instead
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Mr. Cook
SCH 4UM
Charles Law Lab
Jeff Cui, Isaac Chandra, Eli Deng
Complete Data Table: Temperature, Length of Trapped Gas, Averages and Standard Deviation
Temperature ± 0.5 𝐾
Iteration 1
Iteration 2
Iteration 3
Iteration 4
Iteration 5
Length of Trapped Gas ± 0.05 𝑐𝑚
Trial 1
Trial 2
Trial 3
4.95
5.20
5.60
5.95
6.30
4.90
5.20
5.60
5.95
6.30
4.90
5.20
5.60
6.05
6.35
275.0
293.0
313.0
333.0
353.0
Average Length
of Trapped Gas
± 0.05 𝑐𝑚
4.92
5.20
5.60
5.98
6.32
Standard Deviation
of Trapped Gas
(𝑐𝑚)
0.02
0.00
0.00
0.05
0.02
Table 1: This table displays the unprocessed data (temperature and length of trapped gas) as well as processed data
(average length of trapped gas and standard of deviation respectively). Each iteration was performed on
separate days. The tempertature was measured before measuring the length of trapped gas. Addtionally the
standard deviation was lower or equal in all our measurements and therefore for simplicty sake and for
accuracy the reading error will be used from here on out as the assiotated error which is +/- 0.05 cm which
is also the least count of the ruler that was used
Average Length of Trapped Gas Relative to Temperture
Average Length of Trapped Gas +/- 0.05 cm
7,00
Line of Best Fit Gradient
6,00 y = 0.0183x - 0.129
R² = 0.9986
Minimum Gradient
5,00 y = 0.0167x + 0.384
4,00
Maximum Gradient
y = 0.0192x - 0.422
3,00
2,00
1,00
0,00
-50,0
0,0
-1,00
50,0
100,0
150,0
200,0
250,0
300,0
350,0
400,0
Average Temperature of Trapped Gas +/- 0.5 k
Graph 1: This graph is a visual representation of the average temperature of the trapped gas in relation to the length
of the trapped gas as well as the extrapolation of the linear trend back to the x-intercept (0 K absolute
zero). From the graph you can find x-interception of the 𝑚𝑖𝑛 𝑥 − 𝑖𝑛𝑡 = −23.009 𝐾, 𝑚𝑎𝑥 𝑥 − 𝑖𝑛𝑡 =
21.934 𝐾 gradient and line of best fit gradient of 7.05 K. The vertical and horizontal reading errors were
the reading error of +/- 0.05 cm and +/- 0.5 K respectively as the it was greater than the standard
deviation however is too small to see but are nonetheless there. The graph shows the line of best fit and its
corresponding formula 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡𝑟𝑎𝑝𝑝𝑒𝑑 𝑔𝑎𝑠 = 0.0183 𝑐𝑚 𝐾 −1 (𝑡𝑒𝑚𝑝𝑒𝑟𝑡𝑢𝑟𝑒 (𝐾)) − 0.129 𝑐𝑚 and
its 𝑅2 = 0.9986. The 𝑅2 𝑜𝑓 0.9986 significantly signifies a strong positive linear correlation between the
temperature of the trapped gas and its length. Therefore, the reliability of the line of best fit is significant as
the regression score is very close to 1 (a perfect fit) and a value of above 𝑅2 = 0.8 is widely regarded as a
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Mr. Cook
SCH 4UM
Charles Law Lab
Jeff Cui, Isaac Chandra, Eli Deng
strong correlation. The trend matches with the current literature on temperature to volume of a gas. This
trend line is a strong positive linear change.
Equation #1: Experimental Absolute Zero Temperature
Exemplar calculation using the line of best fit equation to calculate the experimental temperature where
absolute “zero” occurs
𝑦 = 𝑚𝑥 + 𝑏
0 = 𝑚𝑥 + 𝑏
−𝑏
𝑥=
𝑚
−(−0.129 𝑐𝑚)
𝑥=
0.0183 𝑐𝑚 𝐾 −1
𝑥 = 7.04918033 … 𝐾
𝑥 = 7.05 𝐾
Slope Formula
Since we are looking for the x-intercept, we plug
in y=0
Rearrange for x
Substitute values found using unit analysis
𝑏 = −0.129𝑐𝑚 and 𝑚 = 0.0183𝑐𝑚 𝐾 −1
Equation #2: Error in Slope
This is the error in slope for the line of best fit
max 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 − min 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡
2
0.0192 𝑐𝑚 𝐾 −1 − 0.0167 𝑐𝑚 𝐾 −1
=
2
0.0025 𝑐𝑚 𝐾 −1
=
2
= 0.00125 𝑐𝑚 𝐾 −1
= 0.001 𝑐𝑚 𝐾 −1
Δ𝑠𝑙𝑜𝑝𝑒 =
Error in slope formula
Substitute values from table #1
This value is the possible range that the slope may or may not fall into
Equation #3 Unit Conversion from Kelvin to Celsius
𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 (℃) = 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 (𝐾) − 273
= 7.05 𝐾 − 273
= −265.95 ℃
This is necessary for the next calculation to get a nonundefined value
To convert from Kelvin to Celsius you
subtract 273
Equation #4 Percentage Error done in Celsius
𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 (℃) − 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙(℃)
% 𝑒𝑟𝑟𝑜𝑟 = |
| × 100%
𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙(℃)
= 265.95℃ − (−273℃)
% 𝑒𝑟𝑟𝑜𝑟 = |
| × 100%
−273℃
% 𝑒𝑟𝑟𝑜𝑟 = 2.58%
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Formula for percentage error
Substitute values using the
experimental value in Celsius and
the theoretical value of -273℃
Mr. Cook
SCH 4UM
Charles Law Lab
Jeff Cui, Isaac Chandra, Eli Deng
We substituted the newly calculated experimental value of = −265.95℃ to work around the theoretical
value of being 0 which gives us an undefined value so therefore we must use Celsius. This does not
impact the values as it is only a conversion of units and not a change of its actual real-world value.
Summary Statement
The Charles lab experiment was a way for us to roughly calculate absolute zero. This constant was found
to be 7.1 ± 0.5 𝐾. Although the actual value of absolute zero (T=0 K) value does not fall between the
error value, this can be explained because the volume of particles cannot realistically become zero.
Additionally, the value is reasonably acceptable as the actual value of absolute zero because it falls
between the min and max absolute value of 𝑚𝑖𝑛 = −23.009 𝐾 and 𝑚𝑎𝑥 = 21.934 𝐾 and is further
supported by the small percent error of only 2.58%. However, some control factors were not taken
account which may explain difference between experimental and theoretical values for example the
pressure of the room was not controlled as a variable. Furthermore, temperature rapidly varies after
removing from the liquid and since measuring didn’t take place instantly after removing from the
heated/chilled liquid, more error is introduced. Overall, for the rigor of a grade 12 class, in a holistic view
the lab was performed overall satisfactorily, and in which had produced somewhat accurate results.
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Mr. Cook