Heat and Thermodynamics

Degree of freedom

The degree of freedom of a dynamic system implies the total number of independent coordinates required to specify the dynamic position of a particle or number of independent motions possible in it. A body having translational motion only has three degrees of freedom. A body which has rotational motion in addition to its translational motion will have six degrees of freedom-three for translational and three for rotational motion.

According to theorem of equipartition of energy, the energy of a system in thermal equilibrium is equally divided among all degrees of freedom.

Each degree of freedom contributes the same amount of average energy to the total, per molecule.

Total translational kinetic energy of N molecules of gas,

= N = =

Where n is number of mole of a gas.

Internal energy of a monoatomic gas is U = .

Internal energy of a diatomic gas is U = .

Real gases:

Deviate at least slightly from idea gas law because of two factors.

  1. Gas molecules attract one another.
  2. Gas molecules occupy a finite volume.

Both of these factors are neglected in the ideal gas law. Both increase in importance when molecules are close together (high P, low T).The real gases obey the van der Waal's equation instead of ideal gas equation.

(V - nb) = nRT

Where corrects for the attraction between molecules.

nbcorrects for the volume of gas molecules.

a and bare called van der Waal's constants.

When a gas is in the state of inequilibrium then the mass, energy and linear momentum of the partice of the gas are transferred from one place to another. This transfer is known as transport phenomenon.

Diffusion phenomenon take place in the gases due to transport of mass.

Viscosity is due to the transport of linear momentum between different layers of the gas.

Heat conduction take place due to the transport of energy in the gases.

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

If n is the number of molecules per unit volume of the gas and d is molecular diameter, then the mean free path is given by

= .

For air molecules at sea level, = m or 0.1 mm. At an altitude of 100 km, the density of air has dropped to such an extend that = 16 cm.


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