Formula and Derivation of Boyle’s Law
Here, ‘P‘ represents the pressure exerted by the gas, ‘V‘ represents the volume of the gas, ‘m‘ represents the mass of each molecule of the gas, ‘n‘ represents the total number of molecules present in volume V and, ‘u‘ represents the root mean square speed of the gas
The kinetic gas equation is written in the form of PV=\frac{1}{3}mnu^2
Rewrite the above equation.
Total mass of the gas (M) is the product of mass (m) of each molecules of the gas and total number of molecules (n) present in volume V.
The kinetic energy of the gas (K.E) is calculated by
Since the molecules are moving with different velocities, they possess different kinetic energies. However, the average kinetic energy of the molecules of a gas is directly proportional to the absolute temperature of the gas.
K.E ∝ absolute temperature of the gas (T)
K.E = kT
Therefore,
Here, 2/3 is a constant, k is called as constant of proportionality.
If Temperature (T) is kept constant then is constant.
Hence, PV = constant
This is the Boyle’s Law
Boyle’s Law
The English chemist Robert Boyle (1627–1691), widely regarded as one of the pioneers of the modern experimental science of chemistry, is commonly credited with this development. He found that increasing the pressure of a sample of contained gas by two times while holding its temperature constant reduced the gas volume by half. According to Boyle’s law, a gas’s volume changes inversely with pressure when the temperature is held constant. This is an illustration of an inverted relationship. The second variable drops when one variable rises in value.