Statistical Mechanics

Statistical mechanics is a branch of physics which applies the probability theory to the study of thermodynamic behaviors of a system with a large number of particles. It provides a framework for relating the microscopic properties of atoms to the macroscopic overall properties of the material. Therefore, statistical mechanics is very useful when explaining thermodynamic properties as a result of classical and quantum mechanical descriptions of statistical and mechanics at a microscopic level.

Statistical mechanics gives a molecular-level interpretation of macroscopic thermodynamic properties such as free energy, entropy, work and heat. The bulk material thermodynamic properties can be studied with regards to the individual molecules. The two central quantities in statistical thermodynamics are the Boltzmann factor and the partition function.

Boltzmann factor
P(E_i )= 1/Z exp^(-βE_i)

Where

β= 1/(k_B T)

Partition Function

Z= ∑_s e^(-βE_s )

Where

β= 1/(k_B T)

These equations are the basic equations of statistical mechanics. These equations were derived in 1870 when studying the Gas Theory by Ludwig Boltzmann. The fundamental postulate for statistical mechanics is

“Given an isolated system in equilibrium, it is found with equal probability in each of its accessible microstates. “ – [1]

This postulate is important due to its ability to allow one to conclude that for a system at equilibrium, the macrostate could result from the largest number of microstates which is also the most probable macrostate of the system.

BrainMass Solutions Available for Instant Download

Approach to demonstrating causality in traffic circle design.

Hello, I have just attached my physics assignment regarding motor vehicle speed and safety with the task sheet along with my teachers feedback. I basically just need to analyse the data more and find more relationships. I was wondering whether anyone would be able to do this. I would like a lot of detail and many relationships

Least square fit of a parabola

Hi, I have attached a problem I would like help with as a picture file. It's not a difficult assignment, but I tend to make "stupid" or careless mistakes when it comes to the more "simple" things, so I would greatly appreciate your help so that I can check my work after I finish and see if I did it correctly and/or identify any

1st, 2nd, 3rd, 4th, 5th, and 6th cumulants in terms of moments

Find the 1st, 2nd, 3rd, 4th, 5th, and 6th cumulants in terms of moments by using the generating function, showing all intermediate steps. For the structure I'm trying to follow, please see attached document, also available from http://ocw.mit.edu/courses/physics/8-333-statistical-mechanics-i-statistical-mechanics-of-parti

Statistical Analysis in Business

1-2. Explain the principles of statistical thinking. Why is statistical thinking an important managerial skill? 1-10.Explain the differences between categorical, ordinal, interval, and ratio data. 1-11. Explain the difference between cross-sectional and time-series data. 1-12. What is the difference between a population a

Some Problems in Statistical Mechanics

Consider a lattice of N particles in an external homogeneous magnetic field, where each particle has two possible energy states, depending on whether the spin of the particle points in the direction of the magnetic field ("down") or opposite to it ("up"). In the "down" state the particle has no energy e = 0 and in the "up" s

Two Seasonal Data Models

C.5. Is it more appropriate to use an additive or a multiplicative model to forecast seasonal data? Summarize the difference(s) between these two types of seasonal models.

Practice Question

Counting without Counting ??? Let me tell you a little dirty secret about the mutual dislike between mathematicians and physicists. It can escalate into a full blown war if diplomacy is not attempted properly. It happens that a graduate student in theoretical/mathematical physics is looking for five members for his disse

Statistical Physics

Please see the attached file: Note only the energies associated with the unzipping have to be considered in the partition function; any energies from the bending, stretching, etc. of the molecule can be ignored. A toy model for DNA molecules. A DNA molecule is made of two complementary strands, which are hold together by hyd

Physics: Use of Debye Model

See attached file for full problem description. 5. a) In lecture we derived the Debye model for the specific heat of a lattice in the customary manner which assumes the same maximum frequency for both transverse and longitudinal waves; hence we introduced a single Debye temperature. Rederive this model permitting different ma

Graduate Statistics problems - MBA program

1. At quickie Car wash, the process is advertised to take less than 7 minutes. Consequently, management has set a target average of 390 seconds for the wash process. Suppose the average range for a sample of nine cars is 10 seconds. Use the below Table 6.1 to establish control limits for sample means and ranges for the car wash

Venn Diagram and Probability problems

A survey of 500 students taking one of more modules in algebra, physics and statistics during one semester revealed the following numbers of students in the indicated modules (see attachment). Draw a venn diagram and show how many students were taking: i) All three modules ii) Algebra or statistics but not physics iii) Al

Time Taken To Melt 2m of Snow

How long would it take sunlight to melt 2 meters (thick) of snow on a mountainside ? Assume that the snow is 50% snow and 50% air, and that the only the sun does any melting (not a good assumption, I knw, but lets do only one thing at a time here). Let the angle of the sun be such that 1000 watts per square meter is incident, bu

Waves, Heat and Light 300 level in Undergraduate

Assume that the phase velocity of waves in some dispersive medium is given as a function of wave length lamda by the relationship see attached Express the group velocity in terms of lamda, v_0 and lamda_0.

Two steady sound waves

Two steady sound waves of equal amplitude but different frequency, traveling in the same direction, are combined. One has a frequency of 188.0 Hz and the other 189.0 Hz. What is the minimum distance between two separated listeners who hear the resulting beat waves in phase (in other words they hear the maxima at the same time)?

Waves, Heat and Light

1. A device called a wave demonstrator consists of rods [moment of inertia of each is I (kg m^2) and springs [tortional constant of each is T (N m)] connected with a spacing delta X as shown in the diagram below. a) Derive a wave differential equation for the angular displacement theta (x,t) b) Show that the wave propagation

Waves, Heat and Light 300 level in Undergraduate

The Helmholtz Resonator- What determines the characteristic frequency when you blow over the top of a bottle? A simple theory, without even appealing to the idea of normal modes was worked out by Helmholtz. The idea is to treat the air in the neck of the bottle as a moving mass and the air in the bulk of the bottle as a spring.

Waves, Heat and Light 300 level in Undergraduate

This course is the third in a three-term introductory physics sequence. The topics covered in this course include: I. Heat and Thermodynamics, II. Wave Phenomena, and III. Introduction to Special Relativity. These topics are essential for understanding a wide range of physical phenomena, and form the basis for modern physics, in

Tension in a string with standing waves and anti-nodal oscillations

The two ends of a uniform string of length 1.4m and mass 8.0gm are fixed. A standing wave is excited on this string with a total of 5 nodal points (including those at the two ends). An anti-nodal point on the string oscillates with an amplitude of 2.0 cm and a maximum speed of 6.0m/s. What is the tension in the string (in N)?

Waves, Heat and Light: Displacement of tranverse waves

See attached file for full problem description. This course is the third in a three-term introductory physics sequence. The topics covered in this course include: I. Heat and Thermodynamics, II. Wave Phenomena, and III. Introduction to Special Relativity. These topics are essential for understanding a wide range of physical p

Waves, Heat and Light: The wave equation

Waves, Heat and Light

Questions on partition function from 'Fundamentals of STATISTICAL AND THERMAL PHYSICS'

Questions on partition function from 'Fundamentals of STATISTICAL AND THERMAL PHYSICS'. See attached file for full problem description.

'Fundamentals of STATISTICAL AND THERMAL PHYSICS'

Thank you so much. I attached my question. My first question, Delta function problem is problem of "Introduction to Elementary Particles", and partition function problem is a problem of 'Fundamentals of STATISTICAL AND THERMAL PHYSICS' I hope attached pictures could help you to solve problem.

Experimental power plant: Natural Energy Laboratory

An experimental power plant at the Natural Energy Laboratory of Hawaii generates electricity from the temperature gradient of the ocean. The surface and deep-water temperatures are 27 degrees Celsius and 6 degrees Celsius respectively. a) What is the maximum theoretical efficiency of this power plant? b) If the power plant

Fundamentals of STATISTICAL AND THERMAL PHYSICS

(See attached file for full problem description)

Statistical Events Random Graduates

12) The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows: Major Male Female Totals Physics 25 25 50 Chemistry 60 40 100 Geology 30 20 50 Totals 115 85 200 Suppose a person is selected at random f