This law describes the volume-temperature relationship of gases at constant pressure. It was put forwarded by the French chemist Jacques Charles in 1787 and was further developed in 1802 by Joseph Gay Lussac. This law can be stated as:

The volume of the fixed mass of a gas at constant pressure is directly proportional to the temperature on Kelvin scale.

**MATHMATICAL INTERPRETATION**

Mathematically, the law may be expressed as

V – T or V = K_{2} T (Pressure and mass constant)

or V / T = K_{2}

where k^{2} is constant of proportionality whose value depends on pressure and amount of gas and the units in which V is expressed.

Let V ^{1} be the volume of a certain mass of a gas at temperature T ^{1} and at pressure P. If temperature is changed to T^{2} keeping pressure constant, the volume changes to V

The relationship between four variables V^{I}‘ T_{1} V^{2} and T is:

V_{1} / T_{1} = V_{2} / T_{2}

**GRAPHICAL REPRESENTATION OF CHARLES’**

The law can also be illustrated by volume-temperature curves. Fig. 15.6 (a) gives a plot of volume of a given mass of a gas against temperature at constant pressure. It also depicts that volume of a gas at constant pressure is a linear function of its temperature. If we plot a graph of variation of volume with temperature (expressed on kelvin scale) at constant pressure, we get a graph as shown in Fig. 15.6 (b). The curve obtained by plotting volume (V) vs temperature at any given pressure is called isobar. The slopes of various isobars at different pressures are different, however, all these lines on extrapolation meet the temperature axis at 0 (K) or -273.15°C.

**KINETIC T THEORY AND CHARLES’ LAW**

When temperature of the gas is increased, the kinetic energy of the molecules increases ( 1/2 mu^{2} – T) . As a result, the velocity of the molecules increases. Consequently, they collide with the walls of the container more frequently and more vigorously. Therefore, the pressure of the gas is expected to increase. However, if pressure is to be kept constant, the force due to molecular collision on the walls of the container must be kept same. This is only possible if the volume of the gas increases, i.e., gas expands. On the other hand, if the temperature is decreased, the average velocity of the molecules decreases and, therefore, the pressure decreases. To keep the pressure constant, volume of the gas must decrease so that the force due to collisions per unit area remains the same. Thus, it can be concluded that “at given pressure volume of the gas increases with rise in temperature, and decreases with the decrease in temperature.” Hence, volume is directly proportional to the temperature at constant pressure. This is Charles’ Law.

**Fig. 15.7. Effect of increase of temperature.**