The relationship between temperature of a gas and its volume was studied by

**in***Jacques Charles***and was further modified by***1787***in***Gay-Lussac***. They gave a generalization known as***1802***. The Law states that, “***Charle’s Law**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 beV

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

**i.e.**1°c + 1°c = 2°cThen, 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}cV

_{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 }= 0This 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})**/**273V

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

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