Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions.

a) Derive the density of states per unit energy, D(ε).

b) Find the Fermi wavevector, k_F, and the Fermi energy, ε_F, in terms of the number of electrons N and the area of the box, A=L² .

c) Calculate the density of states at the Fermi energy, D(ε_F), expressed in terms of N and A. Calculate the heat capacity, C_V.

Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions.

a) Derive the density of states per unit energy, D(ε).

b) Find the Fermi wavevector, k_F, and the Fermi energy, ε_F, in terms of the number of electrons N and the area of the box, A=L² .

c) Calculate the density of states at the Fermi energy, D(ε_F), expressed in terms of N and A. Calculate the heat capacity, C_V.

Methane gas is diffusing in a straight tube 0.1 m long containing helium at 298 k and a total pressure of 1.01325 x 10^5 Pa. the partial pressure of CH4 is 1.400 x 10^4 Pa at one end and 1.333 x 10^3 at the other end. Helium is insoluble in one boundary, and hence is non diffusing or stagnant. Calculate the flux of methane in kg mol/s m^2

Air is at 100 kPa and 150°C, and undergoes a constant pressure process. The final temperature of the air is 1000°C.

a) Compute the specific volume ratio.

b) Compute the boundary work (kJ/kg)

c) Compute the change in specific internal energy by:
1. Using the tables.
2. Integrating the polynomial (cp)
3. Assuming constant specific heat.

d) Repeat c for specific enthalpy

e) Compute the heat

1. Give a short answer to the following questions:

(a) Define magnetization in terms of magnetic dipoles in matter. What is its unit?

(b) What is Coulomb gauge? Use it to show the normal component of the vector potential must be continuous at the boundary of two materials.

(c) Use one of Maxwell's equations (which one?) to show that E is perpendicular to the wave vector k in a plane electromagnetic wave (easiest to use complex notation).

1. Briefly discuss the boundary between expressing an opinion and defamation.

2. Discuss methods other than filtering to prevent employees from inappropriate use of the Internet at work and whether the approach taken by a large company would be as successful at a small company.

3. Explain the main disadvantages of allowing employees at a given organization to create their own personal blogs to reach out to partners, customers, and other employees, and to improve their corporate image.

*(Explained in greatest depth/detail if possible)*

**(Preferably pertaining to Economist Karl Polanyi's Fictitious Commodities, Embeddedness, and Double Movement theorems)**

Has the Economic and Political sectors in the state of Utah been assimilated by the sentiments of The Church of Jesus Christ of the Latter-day Saints (Mormons) religious beliefs? If so, I wonder not only how it affects Utah’s Economic related well-being, but how the LDS religion affects the entire culture of the state of Utah?