Consider a two energy level system like we approached in class and HW, where the two...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider a two energy level system like we approached in class and HW, where the two energy level are A = 0 and B = b. However, the higher energy state now has a 2-fold degeneracy, while the lower level is non-degenerate (see picture below). The total energy of the system is E, and there are N identical particles. The configuration of one particle does not affect the energy of all other particles (ie the particles are independent from each other). EA = 0. (a) Using the microcanonical ensemble, find the entropy as a function of E and N. Hint: Here, the total number of microstates is the binomial coefficient of choosing NB particles occupying the upper level (similar to the treatment in lecture notes), multiplied by the degeneracy for each particle in the upper energy level (so in this case, multiplied by 2^(NB)). (b) Find the expression for the number of particles occupying the lower and higher energy states (N and NB) as a function of temperature, b, and N. (c) At what value of N do you find the maximum entropy in the system? (d) If the system has energy E = 0.75*N*b, and is brought into contact with a bath at constant temperature T = 500 K, in what direction does the heat flow? Justify your answer. Consider a two energy level system like we approached in class and HW, where the two energy level are A = 0 and B = b. However, the higher energy state now has a 2-fold degeneracy, while the lower level is non-degenerate (see picture below). The total energy of the system is E, and there are N identical particles. The configuration of one particle does not affect the energy of all other particles (ie the particles are independent from each other). EA = 0. (a) Using the microcanonical ensemble, find the entropy as a function of E and N. Hint: Here, the total number of microstates is the binomial coefficient of choosing NB particles occupying the upper level (similar to the treatment in lecture notes), multiplied by the degeneracy for each particle in the upper energy level (so in this case, multiplied by 2^(NB)). (b) Find the expression for the number of particles occupying the lower and higher energy states (N and NB) as a function of temperature, b, and N. (c) At what value of N do you find the maximum entropy in the system? (d) If the system has energy E = 0.75*N*b, and is brought into contact with a bath at constant temperature T = 500 K, in what direction does the heat flow? Justify your answer.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these chemical engineering questions
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...
-
On 1 July 2018 Bear Ltd acquired 100 000 shares in Island Ltd at a price of $10 each. There were brokerage fees of $1500. The closing market price of Island Ltd shares on 30 June 2019which is the...
-
An elevator in the Taipei 101 skyscraper can start from rest and accelerate to a maximum speed of 16 m/s with a constant acceleration of 1.1 m/s2. Through what distance does the elevator move as it...
-
Suppose your company needs to raise $40 million and you want to issue 20-year bonds for this purpose. Assume the required return on your bond issue will be 5.7 percent, and youre evaluating two issue...
-
Derive Equation 8.47. S(t)= 1 ko + i=1 ki [1-et/pi] (8.47)
-
Given the following information, draw the project network. Compute the early, late, and slack times for the project network. Which activities on the critical path have only the start or finish of the...
-
A rock is thrown at a 95.0 angle above the horizontal across level ground. It is thrown from a height of 3.00 m above the ground with a speed of 23.0 m/s and experiences no appreciable air...
-
Based on Figure, Joe, one of your systems analysis team members, made the following entry for the data dictionary used by Marilyns Tours: DATA ELEMENT = TOURIST* * * * PAYMENT ALIAS = TOURIST PAY...
-
How should an organization plan for electrical and networking failures or disruptions? What are some items that an organization should consider when planning for such failures and disruptions?...
-
Complete the following 5-year calculations: Net sales, operating expenses, operating income, and net income of Jiranna Healthcare. Total profit margin, asset turnover, return on assets, and return on...
-
Bill Bostic, Sue Chung, and Sam De Felice were assigned ihe task of explaining the elements of financial management to PNC's board of directors, ard the rext session will deal with capital structure....
-
1. A new computer game at Brian's Store costs $53.95. You can order the game from an online game store for $40.55 plus 15% tax. How much will you save by purchasing the game at the online game store?
-
Bill Gates total excess performance was 3% . His pure selection score was 0% and his interaction effect was 6% . It appears Mr. gates is a pretty good apartment investor and understands his...
-
What differentiates the Original Constitution from the Founders' Constitution?
-
10 Discontinuities: identify and classify f(x) = { [(|x+3|)/(x+3), x -1
-
When is the indirect pattern appropriate, and what are the benefits of using it?
-
With the focus on alternative clean-energy sources, we are moving toward an increased use of fuel cells to operate appliances ranging from computers to automobiles. For example, the hydrogen/oxygen...
-
The initial reaction rate for the elementary reaction 2A + B 4C was measured as a function of temperature when the concentration of A was 2 M and that of B was 1.5 M. a. What is the activation...
-
For the decomposition of cumene discussed in this chapter, if an adsorbing inert is present, how would you compare the initial rate as a function of total pressure when desorption is the RLS, as...
-
The Hagen-Poiseuille equation (Equation 6.11) describes the laminar flow of a Newtonian fluid in a tube. Since a Newtonian fluid is defined by the relation $\tau=\mu \dot{\gamma}$, rearrange the...
-
Derive the relation between the friction factor and Reynolds number in turbulent flow for smooth pipe (Equation 6.34), starting with the von Karman equation for the velocity distribution in the...
-
Evaluate the kinetic energy correction factor $\alpha$ in the Bernoulli equation for turbulent flow assuming the $1 / 7$ power law velocity profile (Equation 6.36) is valid. Repeat this for laminar...
Study smarter with the SolutionInn App