Charle’s Law

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^oc for every one degree rise or fall in temperature.”

Mathematically, the law can be represented as fallows;

Let ‘V₀’ 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

V₁  =  V₀  + (1/273) V₀         where V₁ is volume of gas at 1°c

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

Then,    V₂   =   (V₀  +(1/273) V₀)   + (1/273)  V₀

=  V₀   + (2/273) V₀

Similarly at 3°c

V₃   =  V₀   + (3/273)  V₀

At t^oc

V_t   =   V₀   +  (t/273) V₀

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

V_–1   =   V₀  −(1/273) V₀

At  −2°c

V_–2   =   V₀  − (2/273) V₀

At  −273°c

V_–273    =    V₀  − (273/273) V₀

=    V₀ − V₀  =  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   =  V₀   +  (t/273)  V₀

Or   V_t    = (273 V₀ +t V₀ )/ 273

V_t    =   V₀ (273+t) / 273

If 273 + t   =   T

& 273   =    T₀ (on Kelvin scale)

Then,     V_t   = V₀ T / T₀

Or,      V/T= V₀ / T₀

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 V₁ be the volume of gas at temperature T₁, keeping pressure constant, if temperature is increased to T₂, the volume will change to V₂. Then according to Charles’s law;

     V₁ / T₁ = V₂ / T₂