(a) With the aid of a labelled diagram, describe an experiment to illustrate the relationship between the volume and the temperature of a given mass of air ...

Answer Details

(a) Experiment (Charles law: volume against temperature at constant pressure)

A column of dry air is trapped in a uniform capillary tube sealed at one end by a short thread (index) of concentrated sulphuric acid or mercury. The tube is fixed alongside a metre rule in a water bath and the open end is kept upward so that the trapped air is always at atmospheric pressure (constant pressure). The bath is heated slowly and stirred; at several temperatures read on a thermometer, the length L of the trapped air column (which is proportional to its volume) is measured. A graph of L (or volume) against temperature in degrees Celsius is a straight line which, when produced backwards, cuts the temperature axis at about \(-273\,^{\circ}\text{C}\). This shows that at constant pressure the volume of a fixed mass of gas increases uniformly with temperature.

(b) Since the tube is uniform, volume is proportional to length. Cubical (volume) expansivity at constant pressure:

\[\gamma=\dfrac{L_{100}-L_{0}}{L_{0}\times(100-0)}=\dfrac{18.7-13.7}{13.7\times100}=\dfrac{5}{1370}=3.65\times10^{-3}\,\text{K}^{-1}.\]

This is approximately \(\dfrac{1}{274}\,\text{K}^{-1}\), close to the ideal-gas value \(\dfrac{1}{273}\).

(c) By the kinetic theory, raising the temperature increases the average kinetic energy and hence the average speed of the gas molecules. They strike the walls harder and more frequently, tending to raise the pressure. To keep the pressure constant, the gas must expand so that the molecules travel farther between collisions with the walls; thus the volume increases with temperature.