- Level: International Baccalaureate
- Subject: Physics
- Word count: 1211
Charles Law Research Question: Investigate the relationship between the length of a column of air and its temperature in Celsius and by doing so, find a value for Absolute Zero.
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Charles' Law
Research Question: Investigate the relationship between the length of a column of air and its temperature in Celsius and by doing so, find a value for Absolute Zero.
The Absolute Zero is defined as the temperature at which a substance have minimum internal energy, and at the lowest temperature possible. It is often measured in Kelvin, where 0K = -273°C.
To find the Absolute Zero, a linear graph is needed.
Where y = mx + c
The x-intercept is the Absolute Zero, therefore -c/m.
Data Collection and Processing
Raw Data: | L1 |
Temperature ± 0.5°C | Length of Column of Air from Bottom of Capillary Tube ± 0.1cm |
21 | 3.3 |
31 | 3.4 |
41 | 3.5 |
51 | 3.7 |
61 | 3.9 |
71 | 4.1 |
81 | 4.4 |
91 | 4.9 |
100 | 5.6 |
Temperature Uncertainty:
Uncertainty of a thermometer, or any calibrated instrument in fact, is often half the smallest division. The smallest division on a thermometer is 1°C, half of it, is 0.5°C. The uncertainty in the thermometer is therefore ± 0.5°C.
Uncertainty in the Metal Ruler:
The smallest division on the metal ruler is 0.1cm; half the smallest division on the metal ruler is 0.05cm. The result could therefore be stated as: 3.3 ± 0.05cm.
However, we must take into account that a length is a measure of two different positions, then a subtraction of the two. The end of the capillary tube of air may not be exactly on the zero of the ruler. Consider two different alternatives to the initial length of column of air measure from the bottom of the capillary tube:
Length of the Column of Air: (5.3 ± 0.05)cm – (2.0 ± 0.05)cm
From the above, it can be deduced that the length can be between:
(5.3 + 0.05)cm – (2.0 – 0.05)cm and (5.3 – 0.05)cm – (2.0 + 0.05)cm
= 3.4cm and 3.5cm
The range of the possible results is 0.2cm, this can be deduced into
Length of Column of Air = 3.3 ± 0.1cm
Temperature ± 0.5°C | Length of Column of Air from Bottom of Capillary Tube ± 0.1cm | Percentage Error |
21 | 3.3 | 3.03% |
31 | 3.4 | 2.90% |
41 | 3.5 | 2.90% |
51 | 3.7 | 2.70% |
61 | 3.9 | 2.60% |
71 | 4.1 | 2.40% |
81 | 4.4 | 2.30% |
91 | 4.9 | 2.04% |
101 | 5.6 | 1.80% |
Percentage Error:
However, we must also consider the uncertainties in the calculations, indefinitely the percentage error of average length of column of air:
{[(a/L1) + (b/L2) + (c/L3)] / number of trials} *100 = Percentage Error ave
eg. {[(0.1/3.3) + (0.1/2.8) + (0.1/3.1)] / 3} *100 = 1.6%
Error Bars:
(3.03 + 2.9 + 2.9 + 2.7 + 2.6 + 2.4 + 2.3 + 2.04 + 1.8)/9 = 2.2%
Equation: f(x) = 0.03x + 2.5
Gradient: 0.03
Maximum Gradient:
Points on the maximum gradient: (20, 3.2) and (100, 5.7)
Gradient: 0.031
Minimum Gradient:
Points on minimum gradient: (20, 3.4) and (100, 5.5)
Gradient: 0.026
Absolute Zero:
If we change the water temperature, and allow the column of air with Sulphuric Acid Index in it, the results are as shown by the graph on page three.
Creating the extrapolation from the graph, the absolute zero value is calculated:
From the Linear Regression of f(x) = 0.01x + 3.03
Where x intercept = -c/m, we substitute from the function in the graph: = -3.03/0.01.
The linear line intercepts x at -303°C, of which was the closest regression possible to the predicted -273°C.
Conclusion and Evaluation
Conclusion:
The conclusion of this investigation can be expressed through Charles' Law: as the volume of a fixed mass of gas at constant pressure is directly proportional to the absolute temperature. The Absolute Zero can only be a calculated value; the regression is an extrapolation until the x axis is intercepted. This is reinstated by the graphs drawn in previous pages, where a linear regression is shown.
Consistent throughout the experiment, systematic errors occurred. One of which may be from the way the capillary tube was never aligned to the metal ruler. This would cause a systematic error in the reading of the length of column of air. Additionally, would be through the time gaps between the reading of the temperature and the reading of the length of column of air.
Noted from the graph, anomalies occurred from 80°C towards boiling point; there was an acceleration of expansion of column of air unforeseen. The uncertainty in the cross-section of the capillary tube must also be considered, as its diameter could have expanded during the experiment. Water pressure may be differed, hence affecting the results greatly, as the pressure at constant volume is directly proportional to the absolute temperature as the volume is at constant pressure.
There was a difference between the line of best fit and the regression constructed to find the Absolute Zero. Two points from the set of readings were carefully selected, of which together creates the closest value to the estimated Absolute Value (-273°C). This had to be done perhaps due to the anomalies and errors that had occurred during the experiment. The estimated Absolute Value of -273°C is the calculated extrapolation by the Charles' Law.
Evaluation:
The procedure used in data collection had been successful in terms of the interesting readings that can be analyzed. The value of the Absolute Temperature, though in many ways inaccurate, had been calculated successfully. There was a general pattern in the graphs, where it shows clear linear regression, excluding the anomalies. However, if referred to the overall quality of the experiment, there is much that could be improved.
A spirit level could be used to be sure the metal ruler, thermometer, and most importantly the capillary tube was adjacent to the bench. In addition, the angle of which the eye reads the temperature and the metal ruler could be differed. Because of the small imperfections in the experiment, much systematic error had been induced. In addition, perhaps it would be more wise to do two to three more trials, if time precedes, to calculate averages in hopes to reduce random error.
Improvements:
Time gaps between the reading of the temperatures and the lengths could be reduced by ensuring the temperatures are not fluctuating before reading the metal. This can be controlled through the reduction of heat from the bunsen burner. If the heat transferred to the water was controlled, then the control of fluctuation would decrease. By doing so, the readings of the column of air can be more accurate. The anomalies from 80°C onwards could be removed.
A cap could be used to cover the beaker to prevent water loss, which would affect water pressure. The anomalies from 80°C onwards may be caused by this, as that is when water prepares for the breaking of bonds to form into vapour.
Random error could be reduced by taken more trials. From that, we can eliminate anomalies. The calculated Absolute Temperature would also be more accurate.
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