One of the first quantitative observations of gases at different temperatures was made by Jacques Alexandre Charles in 1787. Later John Dalton and Joseph Louis Gay-Lussac continued these kinds of experiments, which showed that a sample of gas at a fixed pressure increases in volume linearly with temperature. By 'linearly' we mean that if we plot the volume occupied by a given sample of gas at various temperatures, we get a straight line.
When you extrapolate such straight lines backwards - you find that they all intersect at a common point. This point occurs at a temperature of -273.15 oC, where the graph indicates a volume of zero. The fact that the volume occupied by a gas varies linearly with degrees Celsius can be expressed mathematically by the following equation:
V = a + bt
Where t is the temperature in degrees Celsius and a and b are constants that determine the straight line. You can eliminate the constant a by observing that V = 0 at t = -273.15 oC for any gas. Substituting into the preceding equation, you get 0 = a + b(-273.15) or a = 273.15b. The equation for the volume can now be rewritten:
V = 273.15b + bt = b(t + 273.15)
Suppose you use a temperature scale equal to degrees Celsius plus 273.15, which you may recognize as the Kelvin scale. K = oC + 273.15. If you write T for the temperature on the Kelvin scale, you obtain V = bT. This is Charles's law, which we can state as follows: the volume occupied by any sample of gas at a constant pressure is directly proportional to the absolute temperature. Thus, doubling the absolute temperature of a gas doubles its volume. We can express this mathematically as follows.
Charles's law: V/T = b (a is a constant for a given amount of gas at a fixed pressure)
An equivalent way of writing Charles's law that is useful for problem solving is the following equation.
Where T is temperature in kelvins, the subscript i denotes initial temperature and volume and the subscript f denotes final temperature and volume.