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Physics

Thermodynamics

Investigating 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

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.

Variables

Independent Variable

Dependent Variable

Temperature in Â°C:

1. 21Â°C

2. 31Â°C

3. 41Â°C

4. 51Â°C

5. 61Â°C

6. 71Â°C

7. 81Â°C

Length of column in mm

Controls

Ambient Pressure â€“ 1 Atm

Mass of air

Humidity ...view middle of the document...

Hence 2Â°C/2 = 1Â°C

I have put the temperature on the x axis and the length of the column on the y axis since the temperature is the independent variable and the length of the column is the dependent variable and has more significant errors, which is easier to plot on the y axis.

Using the results and data from the graph, the x-intercept of the graph, i.e. the value of absolute zero can be deduced

Line of best fit

Minimum Gradient Graph

Maximum Gradient Graph

Equation (where y=length of column in mm & x=Temperature in Â°C

y = 0.25x + 36.964

y = 0.2333x + 39.1

Y = 0.3x + 35.7

x value at x-intercept/ Â°C

- 148

- 125

- 119

y = 0.25x + 35.964 has its x-intercept when y=0

hence, 0 = 0.25x + 35.964

- 0.25x = 35.964

x = 35.964/(-0.25)

x = - 125 Â°C

Hence, the value of absolute zero deduced from the experiment is as follows;

Absolute Zero = (Maximum Absolute Zero + Minimum Absolute Zero) / 2 Â± Uncertainty

= (- 119 â€“ 125)/2 Â± 3

= - 122 Â± 3 Â°C

* Uncertainty = (Maximum Absolute Zero + Minimum Absolute Zero)/2

= (-119 + 125)/2

= 6/2 = 3 Â°C

Conclusion

In conclusion, the results of this experiment show that the graph of the results form a straight line, albeit the result for 81Â°C could be argued as an anomaly. This is because at high temperatures, such as 71Â°C and 81Â°C, the pressure of the gas is higher than normal, which was what I sought to avoid, and thus influence the volume (or the length of the column). If the unit of temperature were to be in Kelvin, the two variables would have been directly proportional. This obeys the Charlesâ€™ Law, which states;

The value of absolute zero calculated from the experiment is -122 Â± 3 Â°C. This has a percentage uncertainty of 3/122 Ã— 100 = 2%, which can be suggested that the experiment was precise. However, considering that the accepted value for absolute zero is -273.15Â°C, the value that I found is very significantly inaccurate. In fact, the percentage error of the value I found from the accepted value is (-273 + 122)/(-273) Ã— 100 = 60 %. This suggests that there were many random and systematic errors.

The biggest source of error in the experiment is the failure to maintain the ambient pressure of the gas inside the glass column. As gas pressure greatly influences the volume (or the length of a capillary column), this would have produced significant random errors, especially across high temperatures. This could be interpreted from the results at 81Â°C, where the length of the column is slightly higher than the norm.

Another random error comes from human error, since I had to determine the point at which I measure the length of the column. There are two possible human errors that could occur. First, I could have misread the temperature correctly...

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