This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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5a. Kinetic theory of gases based on microscopic behaviour of molecules: The kinetic theory of gases is based on the following postulates regarding the microscopic behaviour of gas molecules: 1. Gas consists of very large number of molecules which are in continuous erratic (random) motion. 2. The volume of the molecule is negligibly small compared to the volume occupied by the gas. 3. The molecules do not exert any force on one another except during collision. 4. The collision between molecules and between molecules and the wall of container are perfectly elastic. 5. The time taken during collision is negligibly small. 5b. Equipartition of energy and mean free path: Equipartition of energy: According to the principle of equipartition of energy, every molecule of a gas has (1)/(2)kT average energy per degree of freedom where k is Boltzmann constant and T is absolute temperature. For translational motion there are 3 degrees of freedom, so average kinetic energy per molecule =(3)/(2)kT. Mean free path (): It is the average distance travelled by a gas molecule between two successive collisions. = (1)/(sqrt(2)\,\,d^2)\,n where d is diameter of molecule, n is number of molecules per unit volume. (i) Explain conduction, convection and radiation: Conduction: It is the process of transmission of thermal energy due to molecular collisions without the bulk motion of matter. It occurs mainly in solids. Heat current H = (Q)/(t) = (kA T)/(l) where k is thermal conductivity, A area, T temperature difference, l length. Convection: It is the process of transmission of thermal energy by means of bulk motion (circulation currents) of matter. It occurs in fluids (liquids and gases). Radiation: It is the process of transmission of thermal energy in the form of electromagnetic waves without any material medium. All bodies emit radiation. Stefan's law of black body radiation: The rate of emission of radiant energy by a black body is directly proportional to fourth power of its absolute temperature. Total energy radiated per unit time by black body surface of area A, P = A T^4 where =5.67×10^-8 W m^-2 K^-4 is Stefan's constant. (ii) State Stefan's law: (already stated above) c. Explain diffusion and rate of diffusion: Diffusion: It is the process of net movement of the particles of matter from a region of their higher concentration to a region of lower concentration due to their random motion. It occurs in all states but is fastest in gases, slower in liquids and slowest in solids. Rate of diffusion: According to Graham's law of diffusion, the rate of diffusion of a gas is inversely proportional to the square root of its density (or molar mass). r_1r_2=sqrt(d_2)d_1=sqrt(M_2)M_1 where r is rate of diffusion, d density, M molar mass.