The relationship between temperature of a gas and its volume was studied by *Jacques Charles *in *1787 *and was further modified by *Gay-Lussac *in *1802*. They gave a generalization known as *Charle’s Law*. The Law states that, “*At constant pressure, the volume of a given mass of gas increases or decreases by 1/273 of its volume at 0*^{o}c for every one degree rise or fall in temperature.”

Mathematically, the law can be represented as fallows;

Let ‘V_{0}’ be the volume of given mass of gas at 0°c when temperature is increased by one degree i.e. 1°c, then volume of gas according to Charles law would be

V_{1 }= V_{0 }+ (1/273) V_{0 } *where V*_{1} is volume of gas at 1°c

If temperature is further increased by 1°c **i.e. **1°c + 1°c = 2°c

Then, V_{2 }= (V_{0 }+(1/273) V_{0}) + (1/273) V_{0}

= V_{0 }+ (2/273) V_{0}

Similarly at 3°c

V_{3 }= V_{0 }+ (3/273) V_{0}

**At t**^{o}c

V_{t }= V_{0 }+ (t/273) V_{0}

Similarly if temperature is reduced to −1°c, then

V_{–1 }= V_{0} −(1/273) V_{0}

**At −2°c**

V_{–2 }= V_{0} − (2/273) V_{0}

**At −273°c**

V_{–273 }= V_{0 } − (273/273) V_{0}

= V_{0} − V_{0 }= 0

This means that the volume of a given mass of a gas becomes zero at −273°c. In other words, the gas will cease to exist at this temperature.

The same conclusion can also be drawn graphically. Keeping the pressure of the gas constant, a graph is plotted between temperature and volume. Upon extrapolation (produce), the graph meets temperature at −273°c. This means volume of every gas becomes zero at −273°c.

Charle’s law, may be put in another form as fallows;

V_{t} = V_{0 }+ (t/273) V_{0}

Or V_{t } = (273 V_{0} +t V_{0} )**/** 273

V_{t }= V_{0} (273+t) **/** 273

If 273 + t = T

& 273 = T_{0 }(on Kelvin scale)

Then, V_{t }= V_{0} T / T_{0}

Or, V/T= V_{0} / T_{0} _{}

Thus **V / T** = constant

**V / T** = K

V = KT

Or V α T (at constant pressure)

Thus, Charle’s law may also be defined as, “*The volume of a given mass of a gas at constant pressure is directly proportional to the absolute or Kelvin temperature*.”

Let V_{1 }be the volume of gas at temperature T_{1}, keeping pressure constant, if temperature is increased to T_{2}, the volume will change to V_{2}. Then according to Charles’s law;

**V**_{1} / T_{1} = V_{2} / T_{2}