Question

1. Please answer the following questions.

    ?What is equipartition principle? Why is the latent heat of vaporization

     for water so much larger than the latent heat of fusion?

    ?Describe the Gauss's Law. If our space is four dimensional, what will

      you expect the r dependence of the coulomb's law?

Answer 1

A) The equipartition principle states that energy is shared equally amongst all energetically accessible degrees of freedom of a system.Degrees of freedom are associated with the kinetic energy of translations, rotation, vibration and the potential energy of vibrations.

The latent heat of fusion and vaporization both involve the heat required to change the state of a substance without a change in temperature. In the case of the latent heat of fusion it is the heat required to change a substance from a solid (ice) to a liquid (water) or vice versa while the latent heat of vaporization from a liquid (water) to a gas (steam) or vice versa. So latent heat of vaporization is much larger than the latent heat of fusion.

B)Gauss' Law can be described as: the total of the electric flux out of a closed surface is equal to the magnitude of the charge enclosed divided by the permittivity of free space.

E=q/?₀*1/Area

where Area is the surface area of the spherical Gaussian surface enclosing the charge qq notice the field depends on the area and the area of this imaginary surface in three dimensions is 4?r²

In four spatial dimensions the surface area of this imaginary Gaussian sphere is 2?²r³ . The Coulomb’s law here will have a 1/r³ dependence.