Revision: Kinetic Theory of Gases Physics HSC Science Class 11 Tamil Nadu Board of Secondary Education

The square root of the mean of squares of the speeds of all the molecules of a gas at a given temperature is called root mean square speed.

The energy possessed purely by the motion of molecules in an ideal gas, where the molecules are non-interacting and hence there is no potential energy term, making the internal energy of the gas entirely kinetic in nature, is called the kinetic energy (internal energy) of an ideal gas.

The certain minimum value of temperature below which an object cannot be cooled, since the average kinetic energy of molecules has a minimum possible value of zero at this point, is called absolute zero.

The temperature at which the rms speed of molecules of a gas becomes zero (i.e., T = 0 K, v_rms = 0) is called absolute zero.

The square root of the mean of the squares of the speeds of different molecules of a gas is called Root Mean Square Speed (v_rms).

The minimum number of independent coordinates needed to specify the position and configuration of a thermo-dynamical system in space is called the degree of freedom of the system.

The total number of coordinates or independent quantities required to describe the position and configuration of a system completely is called degrees of freedom (dof).

OR

The total number of independent modes (translational, rotational, vibrational) in which a system can possess energy — i.e., the number of independent ways in which a molecule or atom can exhibit motion — is called the degree of freedom.

The maximum three degrees of freedom corresponding to translational motion is called translational degree of freedom.

The number of degrees of freedom that depends on the structure of the molecule, corresponding to rotational motion, is called rotational degree of freedom.

The degree of freedom exhibited at high temperatures corresponding to vibrational motion is called vibrational degree of freedom.

The average distance travelled by the molecule between collisions is called mean free path (λ).

λ = `"kT"/(sqrt(2)π"d"^2"p")`

The average distance travelled by a gas molecule between two successive collisions is called the mean free path.

OR

The distance travelled by a gas molecule between two successive collisions, during which it moves in a straight line with constant velocity, is called free path.

\[v_{rms}=\sqrt{\frac{v_1^2+v_2^2+v_3^2+v_4^2+\ldots}{N}}\]

where v₁, v₂, v₃… are speeds of individual molecules and N = total number of molecules.

f = 3A − B

where:

• A = number of atoms in the molecule
• B = number of bonds between atoms

Let λ₁, λ₂, λ₃,…λ_n​ be the distances travelled by a gas molecule during nn collisions respectively, then the mean free path is:

An ideal or perfect gas is a gas which obeys the gas laws (Boyle’s law, Charles’ law, and Gay-Lussac’s law) at all pressures and temperatures. An ideal gas cannot be liquefied by the application of pressure or by lowering the temperature.

The average energy per molecule of an ideal gas is directly proportional to the absolute temperature T of the gas:

RMS speed varies directly with the square root of temperature:

With rise in temperature, v_rms of gas molecules increases.

RMS speed decreases with increase in molecular weight:

• Independence from Pressure: v_rms​ does not depend on the pressure of the gas at constant temperature. If pressure is increased n times, density also increases n times, but v_rms remains constant (Boyle's Law: p ∝ ρ).
• Atmosphere of Planets: A planet or satellite will have an atmosphere only if v_rms < v_e​ (escape velocity). Moon has no atmosphere because v_rms of its gas molecules is greater than escape velocity (v_e​).