Charle's Law
Jacques Charles in 1787, and later Joseph Gay Lussac, in 1802, took measurements of the volume of a fixed mass of a gas at various temperatures under the condition of constant pressure and found that the volume of the gas is a linear function of temperature on the Celsius scale.
Mathematically, we write it as
V_{t} = a + bt
Where a and b are constants. Equation (5.3) has been plotted in fig.
V_{t} = V_{0} + bt (5.4)
or b = (V_{t}  V_{0})/t (5.5)
Experiments have shown that for each degree rise in temperature, the volume of gas increases by factor of a V_{0}/273.15. Hence, eq. (5.5) becomes
With this, eq. (5.4) becomes
It is convenient to use the absolute temperature scale on which temperatures are measured in Kelvin (after the scientist, Lord Kelvin, who established such a scale theoretically). Adding 273.15 to the Celsius value gives a reading on the scale. Temperature on the Kelvin scale is represented by the symbol T.
Thus
T/K = 273.15 + t/ï½°C (5.7)
With the above expression, eq. (5.6) modifies to
For a given mass of a gas at constant pressure, the volume V_{0} has a constant value. Hence, the above equation can be written as
V_{T} = K_{2}T or V_{T} T (5.9)
Where the constant K_{2} depends on the mass and pressure of the gas. Equation (5.9) is an alternate form of Charles' law, according to which the volume of a given mass of a gas at constant pressure is directly proportional to the absolute temperature. Such behaviour is shown in fig.
(5.10)

Since volume is directly proportional to Kelvin temperature, the volume of a gas should theoretically be zero at zero Kelvin. However, gases liquefy and then solidify before this low temperature is reached. In fact, no substance exists as a gas at temperatures near zero Kelvin though the straightline plots can be extrapolated to zero volume. The temperature that corresponds to zero volume is  273.15Â° C.