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.

Daniel, age 38, is single and has the following income and expenses in 2019:

Daniel's standard deduction for 2019 is $12,200.

a. Classify the following expenses as either "Deductible for AGI", "Deductible from AGI", or "Not deductible".

What is Daniel's gross income and his AGI?
Gross income: $_____
AGI: $______

b. Should Daniel itemize his deductions from AGI or take the standard deduction?
Because Daniel's total itemized deductions (after any limitations) are $_______, he would benefit from ________ .

Daniel, age 38, is single and has the following income and expenses in 2019:

Daniel's standard deduction for 2019 is $12,200.

a. Classify the following expenses as either "Deductible for AGI", "Deductible from AGI", or "Not deductible".

What is Daniel's gross income and his AGI?
Gross income: _____
AGI: ______

b. Should Daniel itemize his deductions from AGI or take the standard deduction?
Because Daniel's total itemized deductions (after any limitations) are ______, he would benefit from _________.

James is an African American heterosexual male who is also a counselor at a community mental-health center. Though James does not outwardly reject others with different sexual orientations, he is not empathetic toward people struggling with sexual identity issues. James feels that homosexuality is morally wrong and against his religious beliefs. However, James understands that as a counselor he must not discriminate against anyone – including sexual minorities. Clarence, a new client, has revealed that he is homosexual and is having difficulty admitting his sexual orientation to his family and others close to him. Clarence has also states he fears being rejected by his church congregation. He states that being abandoned by the church would further “shame his family” but admits that he cannot keep his life a secret anymore. He wants James’s help to embrace his homosexuality and live without shame.
Respond to the following:

For James to genuinely help Clarence, what issues does James need to address at a personal level to refrain from being judgmental of Clarence?

Is it possible for James to be objective enough to help Clarence work toward his goals? Why or why not?