Gases: The Empirical Gas Laws - Temperature

The conventional liquid-in-glass thermometer was invented in the seventeenth century. This bulb-and-tube device is still in use; it is shown in the Figure below. In these thermometers the diameter of the bulb is much greater than the diameter of the tube so that a small change in the volume of liquid in the bulb will produce a large change in the height of the liquid in the tube.Two things were not clear about the thermometer at this time. The first question was what it was that the thermometer measured. As the temperature or "degree of hotness" apparent to one's fingers increased, the height of the liquid obviously did also, and this was useful in medicine for checking fevers, but there was no quantitative measurement made, merely the relative degree of hotness between this and that.The second question was whether the degree of hotness of any particular thing was a constant everywhere so that the temperatures of other things could be measured relative to it. Suggested fixed temperatures included that of boiling water, that of melting butter, and the apparently uniform temperature of deep cellars.
 
Robert Boyle knew of the thermometer, and also was aware that a gas expands when heated, but since no quantitative temperature scale existed he could not, and did not, determine the relationship between degree of hotness (temperature) and volume of a gas quantitatively. Boyle did propose a scale of temperature, suggesting that use of a specific fluid in a standardized thermometer bulb with a capacity of 10,000 units filled at the boiling point of water would give a proper scale if changes were at the one-unit level; that is, one degree would have a volume of 10,001 units. His scale was not adopted.
 
Guillaume Amontons (d. 1705) developed the air thermometer, which uses the increase in the volume of a gas with temperature rather than the volume of a liquid. The air thermometer is an excellent demonstration of Charles' law because the atmosphere maintains a fixed downward pressure above a small mercury plug of constant mass. The volume of a trapped sample of air increases on heating until the pressure of the trapped air equals the pressure of the atmosphere plus the small pressure due to the plug. Nevertheless, Amontons failed to achieve formulation of Charles' law for the same reason as did Boyle: a quantitative scale of temperature was needed.
 
A quantitative scale of temperature could only be developed after it was realized that at a fixed pressure any pure substance undergoes a phase change at a single fixed temperature which is characteristic of that substance. The melting point of ice to water was taken as 0oC and the boiling point of water was taken as 100oC to give our common Celsius scale of temperature.
 
The study of the effect of temperature upon the properties of gases took considerably longer to achieve a simple quantitative relation than did study of the effect of pressure, primarily because the development of a quantitative scale of temperature was a difficult process. However, once such a scale was developed, the appropriate measurements were made, primarily by the French chemist Jacques Charles (1746 - 1823). On the modern Celsius scale and using modern pressure units, a typical set of Charles' 1787 data would appear as shown in the Figure below.
 
The experimental data were formulated into a general law which became known as the law of Charles or Charles' law:
 
At any constant pressure, the volume of any sample of any gas is directly proportional to the temperature.
 
However, as the graph above shows, the volume extrapolates to zero at a temperature of -273.15oC. If this temperature were taken as the zero of a temperature scale then all negative temperatures could be eliminated.  Such a temperature scale is now the fundamental scale of temperature in the SI.  It is called the absolute scale, the thermodynamic scale, and the Kelvin scale. Temperature on the Kelvin scale, and only on the Kelvin scale, is symbolized by T.
 
A useful formula when the volume of one particular sample of gas changes with temperature, is: 
 
V1T2= V2T1
Example: The volume of a sample of gas is 23.2 cm3 at 20oC. If the gas is ideal and the pressure remains unchanged, its volume at 80oC will be given by 23.2 cm3 (353.15 K/293.15 K) = 27.95 cm3.
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