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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
Vt = a + bt            
Where a and b are constants. Equation (5.3) has been plotted in fig. 


If V0 is the volume of gas at 0 ºC, then from eq. (5.3) it follows that a = V0. Hence, eq. (5.3) becomes
                          Vt = V0 + bt     (5.4)
or                       b = (Vt - V0)/t    (5.5)

Experiments have shown that for each degree rise in temperature, the volume of gas increases by factor of a V0/273.15. 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.

T/K = 273.15 + t/C    (5.7)
With the above expression, eq. (5.6) modifies to

For a given mass of a gas at constant pressure, the volume V0 has a constant value. Hence, the above equation can be written as
VT  =  K2T       or        VT T                                 (5.9)

Where the constant K2 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. 
For a given mass of a gas at constant pressure, Charles' law gives
Where V1 and V2 are the volumes of the gas at temperatures T1 and T2, respectively.
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 straight-line plots can be extrapolated to zero volume. The temperature that corresponds to zero volume is - 273.15° C.

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