Explanation of perfect gases using kinetic theory of gases
An ideal gas is a gas whose pressure P, volume V, and temperature T are related by the ideal gas law: PV = nRT, where n is the number of moles of the gas and R is the ideal gas constant.
Using kinetic theory of gases ideal gas equation can be explained.
According to kinetic theory of gases heat energy of a gas is the result of kinetic energy of its molecules. In absolute zero temperature heat energy of molecules of a gas is zero. As a result kinetic energy of the molecules and root mean square velocity also becomes zero. When heat is supplied to a gas, it appears as the kinetic energy of molecules.
K.E. = ½ mnc2 = ½ Mc2
Here, m = mass of each molecule, n = number of molecules, c = root mean square velocity and M = mn = mass of the gas.
We have seen earlier that average kinetic energy of a gas is proportional to the temperature.
So, We get,
½ mnc2 ∞ T;
or, ½ Mc2 = T
Here, K = proportionality constant.
But from the equation of pressure of a gas we get,
P = 1/3 mnc2/V = 1/3 Mc2/V
or, PV = 1/3 Mc2 = 2/3 x 1/2 Mc2 = 2/3 KT
or, PV = RT
Here, R = 2/3 K = constant
then, PV = RT is called the ideal gas equation.
It is to be mentioned that V = volume of one gm at gas molecules. If n gm gas is considered, then from ideal gas equation becomes PV = nRT. It is proved from the kinetic theory of gases.