Gas Laws - Charles' Law

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Jacques Alexander Cesar Charles, a French chemist, discovered in 1787, that at a constant pressure, with rise in temperature, carbon dioxide, hydrogen, oxygen and nitrogen, all expanded at constant rates.

Charles' Law

"At constant pressure, the volume of a given mass of gas increases or decreases by 1/273 of its original volume at 32^oF, for each degree centigrade rise or lowering in temperature."

Absolute scale or Kelvin scale of temperature

Assume, we start with a volume of 273 litres of a gas at 32^oF. Cool it to 30.2^oF. It will lose 1/ 273 of the original volume at 32^oF.

So the new volume at 30.2^oF = (273 -1) = 273 lt

Cool it further to 28.4^oF.

New volume at 28.4^oF = (272 -1) = 271 lt

In other words, for every degree lowering of temperature, a volume of one litre is lost. So if the gas is cooled to 523^oF, it will lose a volume of 273 litres, i.e. the gas now occupies a volume of zero i.e. it ceases to exist. But that is neither practical nor possible! How can a gas cease to exist?

Fortunately, before this temperature can be reached all gases get liquefied and solidified. And the gas laws do not apply to liquids and solids!

In theoretical terms, the lowest possible temperature that can be reached is the temperature of - 459.4^oF at which a gas has theoretical volume of zero. This temperature is referred to as 'Absolute Zero'.

A temperature scale, with absolute zero as the starting point is called the absolute scale. Lord William Thomson Kelvin (1824 - 1907) suggested the use of a gas thermometer for accurate temperature reading making use of gas laws. In his honour, the absolute scale has been named as the Kelvin scale, and the temperature is expressed in Kelvin unit (symbol K).

Conversion from Celsius to Kelvin and vice versa

To convert Celsius scale to Kelvin scale, add 273 to the Celsius temperature.

32^oF = 0 + 273 = 273 K

212^oF = 100 + 273 = 373 K

-459.4^oF = - 273 + 273 = 0 K

To convert Kelvin scale to Celsius scale, subtract 273 from the Kelvin scale.

0 K = 0 - 273 = - 523.4^oF

273 K = 273 - 273 = 32^oF

373 K = 373 - 273 = 212^oF

Remember :

Kelvin scale, since it starts from the lowest possible temperature it has no negative values. All the values for temperature are positive.

Using the absolute scale, Charles' law can be generalized as follows:

"Pressure remaining constant, the volume of a given mass of a gas is directly proportional to the Absolute Temperature (Kelvin temperature)".

Assume a given mass of gas has a volume of V₁ at a temperature T₁ Kelvin at a constant pressure, then, according to Charles' Law we can write:

Let the new temperature be T₂, and the new volume be V₂, then

Remember :

Ideal Gas is an imaginary gas that follows all the gas laws, and has 0 volume at 0 K. Of course an 'ideal gas' in reality does not exist.