DRAFT: This module has unpublished changes.

Data Analysis and Conclusions:


                The modified Ruchhardt’s method used to determine the heat capacities of Air, Nitrogen, Helium and Carbon dioxide resulted in the following data:

 

 

m(g)

T(s)

x(mm)

V(m3)

p(Pa)

γ

A (m2)

Air

240.14

1.11

1160

0.02076

99000

1.39

 

1.075E-3

Air  Weight

340.14

1.3

1160

0.02076

99000

1.44

 

1.075E-3

CO2

240.14

1.13

1160

0.02076

99000

1.35

 

1.075E-3

CO2 Weight

340.14

1.3

1160

0.02076

99000

1.44

 

1.075E-3

Nitrogen

240.14

1.12

1160

0.02076

99000

1.37

 

1.075E-3

Nitrogen Weight

340.14

1.3

1160

0.02076

99000

1.44

 

1.075E-3

He

240.14

1.06

1160

0.02076

99000

1.53

 

1.075E-3

He Weight

340.14

1.25

1160

0.02076

99000

1.56

 

1.075E-3

The ratio of the heat capacity at constant pressure to that at constant volume (γ) for each gas was calculated from the experimental data using the formula:

 

 

Where m is the mass of the cylinder, V the volume of the tube combined with the volume of the gas reservoir, p the pressure, T the period and A the surface area of the face of the cylinder. In order to achieve a more accurate estimation of γ the period used for each calculation was an averaged period from all of the runs performed for that particular gas.

 

          The predicted value of γ for Air, Nitrogen and Carbon dioxide was 7/5. Yet the experimental values of γ were calculated to be 1.39 and 1.44 for Air, 1.35 and 1.44 for Carbon dioxide, and 1.37 and 1.44 for Nitrogen. The predicted value of γ for Helium was 5/3 but the calculated values were 1.53 and 1.56. Since the experimentally determined values of γ were significantly different from the predicted or known values for each gas that was used, this experiment must have had a large amount of error.

 

          The data obtained from the lab could be poor due to the system not being completely air tight, which would allow for gas to escape. If some of the gas of interest is lost from the apparatus then a mixture of that gas and air would result in the tube. If the gas in the tube is not pure then values obtained from the oscillation of the cylinder would be different from the actual values that should be observed by that particular gas. Another source of error could be due to the fact that each run was not started at the exact same pressure. This deviation in the starting pressure could account for the incorrect γ values that were calculated. In order to determine if the experimental values of the period and its standard deviation obtained for each run were consistent, the statistical F test and T test were used.

 

          The F and T tests compared the average period of all five experimental runs for one person in the lab to the average periods of all the runs of each of the two other people whom performed the lab as well.  The F test for each set of runs for each gas showed that there was little difference between the standard deviations of the periods for each gas between the three sets of results. The T test on the other hand showed that there was a significant difference in the periods for the three sets of data points for Air and Carbon dioxide, which would account for the incorrect values of γ that were calculated. The T test also showed that there was little difference between the periods of the three sets of data for Helium and Nitrogen.  Since the experimental values of γ did not correspond to the known values, the original hypothesis was not supported. Overall the experiment successfully replicated Ruchhardt’s original method, but unsuccessfully calculated the values for the γ of each gas.

DRAFT: This module has unpublished changes.