Gay-Lussac/Charles'law

Joseph-Louis Gay-Lussac investigated the expansion of gases as the temperature is increased. His data helped establish Charles' law, which says, in its modern form, that the volume of a gas is directly proportional to the absolute temperature. (Charles, by the way, is Jacques Charles, who had made some observation on the subject before Gay-Lussac, but never published them.)

1) Gay-Lussac typically began his experiments at the freezing point of water with a volume of 100 (in some unspecified volume units). Use Charles' law to predict the volume of the gas (in the same units) at the boiling point of water.

2) Gay-Lussac found that the volume of gas was 100 when the temperature was 0°C; when the temperature was 100°C, the volume was 137.50. The Kelvin temperature scale had not been developed when Gay-Lussac carried out his experiments. (Indeed, Kelvin had not yet been born.) Gay-Lussac worked with the Celsius temperature scale. Charles' law with the temperature expressed in °C says:

V = mt + b ,
where m and b are constants.
a) Solve for m and b.
b) Use Charles' law and the values of m and b found in part (a) to find the temperature (in °C) at which the volume of a gas would become zero. (Note: this is an estimate of the temperature later called "absolute zero" on absolute temperature scales.)

3) Gay-Lussac made several measurements of the same quantity, as is common procedure in careful work. The following table contains multiple measurements of the volume of atmospheric air at the boiling point of water, expanded from 100 volume units at the freezing point of water and multiple measurements of oxygen under the same conditions.

Atmospheric airOxygen
137.40137.47
137.61137.54
137.44137.45
137.55
137.48
137.57
a) Report the mean mass and standard deviation of the volume of atmospheric air and of the oxygen.
b) Is the small difference between atmospheric air and the oxygen likely to be within experimental error or is it likely to be due to a physical difference between the two sets of samples? Explain with reference to the data.

Reference

Joseph-Louis Gay-Lussac, "The Expansion of Gases by Heat," Annales de Chimie 43, 137 (1802)
Copyright 2003 by Carmen Giunta. Permission is granted to reproduce for non-commercial educational purposes.

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