# Questions on partition function

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

© BrainMass Inc. brainmass.com October 16, 2018, 5:22 pm ad1c9bdddfhttps://brainmass.com/physics/statistical-mechanics/questions-on-partition-function-51352

#### Solution Preview

Your auxiliary picture "4 help.jpg" seems to be answering the 2nd question, but I am not sure of the relevance of "1 help.jpg" to the 1st question, and so I offer a "start from basics" derivation of the relations requested in question 1.

Both the pdf file and its plain tex source are attached

bf Question 1 rm

The probability that a system in thermal equilibrium is in microstate $j$ is

$$

p(j) propto e^{-beta E_j},

$$

where $beta = 1/kT$. The ...

Calculus Help

Let B(x) represent the area bounded by the graph and the horizontal axis and vertical

lines at t=0 and t=x for the graph below. Evaluate B(x) for x = 1, 2, 3, 4, and 5.

f(x)=x^2,g(x)=3x,and h(x)=2/x. Evaluate each sum.

∑_(i=0)^3▒〖f(1+i)〗

sketch the function and find the smallest possible value and the largest possible value for a Riemann sum of the given function and partition.

f(x)=x^2-2x+3

P={0, 1, 2,3}

For f(x)=3+x, partition the interval [0, 2] into n equally wide subintervals of length Δx = 2/n. Write the lower sum for this function and partition, and calculate the limit of the lower sum as n⟶∞ (b) Write the upper sum for this function and partition and find the limit of the upper sum as n⟶∞.

Use the graph to determine the values of the definite integrals. ∫_3^5▒f(x)dx

Same instructions and graph as above. ∫_3^5▒〖|f(x)|dx〗

sketch the graph of the integrand function and use it to help evaluate the integral.

∫_0^2▒〖|x|-1dx〗

use the Antiderivatives and Definite Integrals Theorem to evaluate the integrals.

∫_0^2▒〖4x^3 dx. ∫_0^1▒〖4x^3 dx. ∫_1^2▒〖4x^3 dx.〗〗〗

The velocity of a car after t seconds is 3t^2 feet per second. (a) How far does the car travel during its first 10 seconds? (b) How many seconds does it take the car to travel half the distance in part (a)?

Find the exact area under half of one arch of the sine curve: ∫_0^(π/2)▒〖sin(x)dx〗. (Note: D( -cos(x) ) = sin(x) )

View Full Posting Details