as, mean square speed v kT ( . ) root mean square speed, v rms = kT kT = . ( . ) From the equation ( .
) we infer the following (i) rms speed is directly proportional to square root of the temperature and inversely proportional to square root of mass of the molecule. At a given temperature the molecules of lighter mass move faster on an average than the molecules with heavier masses. From the equation ( . ), pressure is equal to / of mean kinetic energy per unit volume.
. . Some elementary deductions from kinetic theory of gases Boyle’s law: From equation ( . ), we know that PV U = But the internal energy of an ideal gas is equal to N times the average kinetic energy ( ∈ ) of each molecule.
U = N ∈ For a fixed temperature, the average translational kinetic energy ∈ will remain constant. It implies that PV = N ∈ Thus PV = constant Therefore, pressure of a given gas is inversely proportional to its volume provided the temperature remains constant. This is Boyle’s law . Charles’ law: From the equation ( .
), we get PV U = For a fixed pressure, the volume of the gas is proportional to internal energy of the gas or average kinetic energy of the gas and the average kinetic energy is directly proportional to absolute temperature. It implies that V α T or V T = constant This is Charles’ law. Avogadro’s law: This law states that at constant temperature and pressure, equal volumes of all gases contain the same number of molecules. For two different gases at the same temperature and pressure, according to kinetic theory of gases, - - - - Unit Kinetic theory of gases EXAMPLE .
A room contains oxygen and hydrogen molecules in the ratio : . The temperature of the room is °C. The molar mass of is g mol - and of H is g mol - . The value of gas constant R is .