**Charles's Law**

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 ^{o}C,
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 ^{o}C for any gas. Substituting
into the preceding equation, you get 0 = *a* + *b*(-273.15) or *a *=
273.15*b. *The equation for the volume can now be rewritten:

*V *= 273.15*b *+ *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 = ^{o}C + 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.