# 5.5.2 Charles’ Law (Temperature – Volume Relationship)

Charles and Gay Lussac performed several experiments on gases independently to improve upon hot air balloon technology.

Their investigations showed that for a fixed mass of a gas at constant pressure, volume of a gas increases on increasing temperature and decreases on cooling.

They found that for each degree rise in temperature, volume of a gas increases by 1/273.15 of the original volume of the gas at 0 °C.

Thus if volumes of the gas at 0 °C and at t °C are V0 and Vt respectively, then At this stage, we define a new scale of temperature such that t °C on new scale is given by T = 273.15 + t and 0 °C will be given by

T0 = 273.15. This new temperature scale is called the Kelvin temperature scale or Absolute temperature scale.

Thus 0°C on the celsius scale is equal to 273.15 K at the absolute scale. Note that degree sign is not used while writing the temperature in absolute temperature scale, i.e., Kelvin scale.

Kelvin scale of temperature is also called Thermodynamic scale of temperature and is used in all scientific works.

Thus we add 273 (more precisely 273.15) to the celsius temperature to obtain temperature at Kelvin scale.

If we write Tt = 273.15 + t and T0 = 273.15 in the equation (5.6) we obtain the relationship Thus we can write a general equation as follows. The value of constant k2 is determined by the pressure of the gas, its amount and the units in which volume V is expressed.

Equation (5.10) is the mathematical expression for Charles’ law, which states that pressure remaining constant, the volume of a fixed mass of a gas is directly proportional to its absolute temperature.

Charles found that for all gases, at any given pressure, graph of volume vs temperature (in celsius) is a straight line and on extending to zero volume, each line intercepts the temperature axis at – 273.15 °C.

Slopes of lines obtained at different pressure are different but at zero volume all the lines meet the temperature axis at – 273.15 °C.

Each line of the volume vs temperature graph is called isobar.

Observations of Charles can be interpreted if we put the value of t in equation (5.6) as – 273.15 °C. We can see that the volume of the gas at – 273.15 °C will be zero.

This means that gas will not exist. In fact all the gases get liquified before this temperature is reached. The lowest hypothetical or imaginary temperature at which gases are supposed to occupy zero volume is called Absolute zero.

All gases obey Charles’ law at very low pressures and high temperatures.